COMMON SHARE PURCHASE WARRANTS

Exhibit 10.4

THE SECURITIES REPRESENTED HEREBY AND THE SECURITIES ISSUABLE UPON EXERCISE HEREOF HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “U.S. SECURITIES ACT”) OR STATE SECURITIES LAWS. THE HOLDER HEREOF, BY PURCHASING OR OTHERWISE HOLDING SUCH SECURITIES, AGREES FOR THE BENEFIT OF THE CORPORATION THAT SUCH SECURITIES MAY BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED ONLY (A) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE U.S. SECURITIES ACT IN A TRANSACTION COMPLETED IN ACCORDANCE WITH THE REGISTRATION STATEMENT, (B) TO THE CORPORATION, (C) OUTSIDE THE UNITED STATES IN COMPLIANCE WITH RULE 903 OR RULE 904 OF REGULATION S UNDER THE U.S. SECURITIES ACT, (D) IN COMPLIANCE WITH THE EXEMPTION FROM REGISTRATION UNDER THE U.S. SECURITIES ACT PROVIDED BY RULE 144 OR RULE 144A THEREUNDER, IF AVAILABLE, AND IN ACCORDANCE WITH APPLICABLE STATE SECURITIES LAWS, OR (E) IN A TRANSACTION THAT DOES NOT REQUIRE REGISTRATION UNDER THE U.S. SECURITIES ACT OR ANY APPLICABLE STATE SECURITIES LAWS, AND THE HOLDER HAS, PRIOR TO SUCH SALE, FURNISHED TO THE CORPORATION AN OPINION OF COUNSEL OF RECOGNIZED STANDING IN FORM AND SUBSTANCE SATISFACTORY TO THE CORPORATION TO SUCH EFFECT. DELIVERY OF THIS CERTIFICATE MAY NOT CONSTITUTE “GOOD DELIVERY” IN SETTLEMENT OF TRANSACTIONS ON STOCK EXCHANGES IN CANADA. HEDGING TRANSACTIONS INVOLVING THE SECURITIES MAY NOT BE CONDUCTED UNLESS IN COMPLIANCE WITH THE U.S. SECURITIES ACT.

COMMON SHARE PURCHASE WARRANTS

THESE WARRANTS WILL BE VOID AND OF NO VALUE UNLESS EXERCISED BEFORE 4:00 P.M. (CENTRAL STANDARD TIME) ON APRIL 2, 2012.

TRANSATLANTIC PETROLEUM CORP.

(Incorporated under the Business Corporations Act (Alberta))

THIS IS TO CERTIFY THAT, FOR VALUE RECEIVED,

(the “holder”) is entitled to subscribe for and purchase, upon and subject to the terms and conditions hereinafter set forth, one fully paid and non-assessable Common Share (a “Common Share”) in the capital of TransAtlantic Petroleum Corp. (the “Corporation”) (as constituted at April 2, 2009) for each whole warrant (a “Warrant”) represented hereby, at any time on or after the date hereof but prior to 4:00 p.m. (Central Standard Time) on April 2, 2012 (the “Time of Expiry”) at and for a price of US$1.20 per Common Share (the “Exercise Price”).

The right to purchase Common Shares hereunder may only be exercised during the period herein specified by:

Upon surrender and payment as aforesaid, the Corporation will, subject to the terms hereof, issue to the person or persons named in the exercise form the number of Common Shares subscribed for and such person or persons will be shareholders of the Corporation in respect of such Common Shares as at the date of surrender and payment notwithstanding any delay in the issuance of a share certificate in respect thereof. Within five business days after surrender and payment, the Corporation will mail to such person or persons, at the address or addresses specified in the exercise form, a certificate or certificates evidencing the Common Shares subscribed for, or if requested by the holder, make available for pick-up at the Corporation’s office such certificate or certificates within five business days of the satisfaction of the exercise requirements herein. If the holder subscribes for a number of Common Shares which is less than the maximum number of Common Shares which could be subscribed for as the result of the exercise of all of the Warrants evidenced by this Warrant Certificate, the holder shall be entitled to receive a new Warrant Certificate (substantially in the form hereof) for that number of the Warrants not exercised so as to allow the purchase of those Common Shares that might have been subscribed for hereunder but which were not then subscribed for and purchased by the holder.

In no event shall fractional Common Shares be issued in connection with the exercise of the Warrants evidenced by this Warrant Certificate. In lieu of a fractional Common Share that would otherwise be issuable upon an exercise of the Warrants, there shall be paid to the holder by the Corporation, within ten (10) business days after the date of surrender of this Warrant Certificate and satisfaction of the exercise requirements herein, an amount in lawful money of the United States equal to the then current market value of such fractional share computed on the basis of the Current Market Price (as defined below) of the Common Shares on such date of exercise, provided that the Corporation shall not be required to make any payment, calculated as aforesaid, that is less than US$10.00.

“Current Market Price” of the Common Shares at any date means the volume weighted average trading price per share for such shares for the 10 consecutive Trading Days immediately preceding such date on the Toronto Stock Exchange or, if on such date the Common Shares are not listed on the Toronto Stock Exchange, on such stock exchange upon which such shares are listed and as selected by the directors of the Corporation, or, if such shares are not listed on any stock exchange, then on such over-the-counter market as may be selected for such purpose by the directors of the Corporation, and, in the event the Common Shares do not trade on any over-the-counter market, then in such manner as the directors of the Corporation determine, having regard to the parity and equality of the interests of the holders of Common Shares in the Corporation and “Trading Days” means, with respect to a stock exchange, a day on which such exchange is open for the a transaction of business and with respect to an over-the-counter market, a day on which the Toronto Stock Exchange is open for the transaction of business.

The Warrants evidenced by this Warrant Certificate are exercisable at any time and from time to time up to, but not after, the Time of Expiry, upon payment in the manner and at the place provided for above.

Nothing contained herein shall confer on the holder or any other person any right to subscribe for or purchase shares in the capital of the Corporation at any time subsequent to the Time of Expiry and from and after such time the Warrants evidenced by this Warrant Certificate and all rights hereunder shall expire and be of no further force or effect.

If this Warrant Certificate is stolen, lost, mutilated or destroyed, the Corporation shall, on such reasonable terms as to indemnity or otherwise as it may impose, deliver a replacement Warrant Certificate of like denomination, tenor and date as the Warrant Certificate so stolen, lost, mutilated or destroyed.

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The Warrants evidenced by this Warrant Certificate shall not entitle the holder to any rights whatsoever as a shareholder of the Corporation.

The Exercise Price or the number of Common Shares or other securities or property purchasable upon exercise of the Warrants shall be subject to adjustment from time to time in the events and in the manner provided for below:

(each of the events enumerated in the clauses (i), (ii) and (iii), above, being hereinafter referred to as a “Common Share Reorganization”), the Exercise Price shall be adjusted effective immediately after the record date or effective date, as the case may be, which is used to determine the holders of outstanding Common Shares for the happening of a Common Share Reorganization, by multiplying the Exercise Price in effect immediately prior to such record date or effective date by a fraction, the numerator of which shall be the number of Common Shares outstanding on such record date or effective date before giving effect to such Common Share Reorganization, and the denominator of which shall be the number of Common Shares outstanding immediately after giving effect to such Common Share Reorganization (including, in the case of an issuance or distribution of Convertible Securities, the number of Common Shares that would have been outstanding had such securities been converted into Common Shares on such date).

To the extent that any adjustment in the Exercise Price occurs pursuant to this paragraph (a) as a result of the fixing by the Corporation of a record date for the distribution of Convertible Securities, the Exercise Price shall be readjusted immediately after the expiry of any relevant conversion right to the Exercise Price which would then be in effect based upon the number of Common Shares actually issued and remaining issuable after such expiry and shall be further readjusted in such manner upon the expiry of any further such right.

If and whenever at any time after the date hereof and prior to the Time of Expiry a Common Share Reorganization shall occur and any such event results in an adjustment in the Exercise Price, the number of Common Shares purchasable pursuant to each of the Warrants evidenced by this Warrant Certificate shall be adjusted contemporaneous with the adjustment of the Exercise Price, by multiplying the number of Common Shares theretofore purchasable on the exercise thereof by a fraction, the numerator of which shall be the Exercise Price in effect immediately prior to such adjustment and the denominator of which shall be the Exercise Price resulting from such adjustment.

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To the extent that Exchangeable Securities are not exchanged for or converted into Common Shares prior to the expiry thereof, the Exercise Price as determined pursuant to this paragraph (b) will be readjusted to the Exercise Price which would be in effect based upon the number of Common Shares (or other securities) actually delivered on the exchange or conversion of such Exchangeable Securities.

Any Common Shares owned by or held for the account of the Corporation or any subsidiary (as defined in the Business Corporations Act (Alberta)) of the Corporation shall be deemed not to be outstanding for the purpose of any such computation.

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To the extent that such distribution is not so made, the Exercise Price shall be readjusted to the Exercise Price which would then be in effect if such record date had not been fixed or to the Exercise Price which would then be in effect based upon such shares or rights, options or warrants or evidences of indebtedness or assets actually distributed.

Any Common Shares owned by or held for the account of the Corporation or any subsidiary (as defined in the Business Corporations Act (Alberta)) of the Corporation shall be deemed not to be outstanding for the purpose of any such computation.

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On the happening of each and every event referred to above that gives rise to an adjustment, the applicable provisions of these Warrants shall, ipso facto, be deemed to be amended accordingly and the Corporation shall take all necessary action so as to comply with such provisions as so amended. The Corporation shall promptly send to the holder notice of any and all adjustments hereunder as well as any adjustment to the Common Shares of the Corporation pursuant to the terms of the Articles of the Corporation.

The Corporation covenants that, so long as any Warrants remain outstanding it will give notice to the holder of its intention to fix a record date that is prior to the Expiry Time for any event referred to in subsections (a)(i), (b), (c) or (d) hereof which may give rise to an adjustment in the number of Common Shares to be received on exercise or the Exercise Price. Such notice shall specify the particulars of such event and the record date for such event, provided that the Corporation shall only be required to specify in the notice such particulars of the event as shall have been fixed and determined on the date on which the notice is given. The notice shall be given in each case not less than 15 days prior to such applicable record date. The Corporation covenants that it will not close its transfer books or take any other corporate action which might deprive the holder of the opportunity to exercise its right of acquisition pursuant thereto during the period of 15 days after the giving of the notices set forth in this paragraph.

Subject to compliance with all securities laws in regard thereto, the Warrants represented by this Warrant Certificate and all rights granted hereunder shall be assignable and transferable to any party by the holder hereof. Subject to compliance with all securities laws in regard thereto, the holder of this Warrant Certificate may at any time prior to the Expiry Time, upon delivery to the Corporation (in the same manner as provided for exercise) of this Warrant Certificate and a duly completed and executed transfer in the form as attached hereto (the “Transfer Form”), and upon payment of reasonable charges of the Corporation (if requested), transfer and re-register the Warrants represented by this Warrant Certificate into the name of another holder. The Corporation reserves the right to require evidence, to its sole reasonable satisfaction, of compliance with all applicable securities laws prior to giving effect to any assignment or transfer of the Warrants represented hereby.

Within 14 days of receipt of this Warrant Certificate and the duly completed and executed Transfer Form and evidence of compliance with applicable securities law, as provided for above, the Corporation will cause to be mailed or delivered to such person or persons at the address or addresses specified in the Transfer Form, a certificate or certificates evidencing the number of Warrants to be transferred.

Notwithstanding any provision to the contrary contained herein, the Corporation will refuse to register any transfer of this Warrant Certificate not made in accordance with Regulation S of the U.S. Securities Act, pursuant to a registration under the U.S. Securities Act, or pursuant to an exemption from registration under the U.S. Securities Act.

Any notice to the holder shall be valid and effective if delivered or sent by courier or ordinary post to the holder at the address appearing on the face page hereof.

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Notwithstanding any provision to the contrary contained herein, no Common Shares will be issued pursuant to the exercise of any Warrant if the issuance of such securities would constitute a violation of the securities laws of any applicable jurisdiction, and the certificates evidencing the Common Shares thereby issued may bear such legend as may, in the opinion of legal counsel to the Corporation, be necessary in order to avoid a violation of any securities laws of any applicable jurisdiction or to comply with the requirements of any stock exchange on which the Common Shares of the Corporation are listed, provided that, at any time, in the opinion of legal counsel to the Corporation, such legends are no longer necessary in order to avoid a violation of any such laws, or the holder of any such legended certificate, at that holder’s expense, provides the Corporation with evidence satisfactory in form and substance to the Corporation (which may include an opinion of legal counsel satisfactory to the Corporation) to the effect that such holder is entitled to sell or otherwise transfer such Common Shares in a transaction in which such legends are not required, such legended certificate may thereafter be surrendered to the Corporation in exchange for a certificate which does not bear such legend.

The Corporation represents and warrants that it is duly authorized to create and deliver these Warrants and to issue the Common Shares that may be issued hereunder and that these Warrants, when signed by the Corporation as herein provided, will be a valid obligation of the Corporation enforceable against the Corporation in accordance with the provisions hereof. The Corporation hereby covenants and agrees that, subject to the provisions hereof, it will cause the Common Shares from time to time duly subscribed for and purchased in the manner herein provided, and the certificates evidencing such Common Shares, to be duly issued and delivered, and that at all times up to and including the Time of Expiry, while these Warrants remain outstanding, it shall have sufficient authorized capital to satisfy its obligations hereunder should the holder determine to exercise the right in respect of all the Common Shares for the time being purchasable pursuant to the Warrants. All Common Shares issued upon the exercise of the right to purchase herein provided (upon payment therefor of the amount at which such Common Shares may at the time be purchased pursuant to the provisions hereof), shall be issued as fully paid and non-assessable Common Shares.

The Corporation represents and warrants that it has requested that the Common Shares issuable hereunder be listed and posted for trading on the Toronto Stock Exchange (the “TSX”) and has received the conditional approval of the TSX therefor. The Corporation covenants to use its reasonable best efforts to ensure that the conditions set forth in such approval are satisfied as soon as practicable.

Time shall be of the essence hereof.

The Warrants evidenced by this Warrant Certificate shall be governed by and construed in accordance with the laws of the Province of Alberta and the laws of Canada applicable therein and shall be treated in all respects as an Alberta contract.

The Warrants evidenced by this Warrant Certificate shall not be valid for any purpose whatsoever until signed by the Corporation.

IN WITNESS WHEREOF the Corporation has caused this Warrant Certificate to be executed and delivered by its proper officer, duly authorized in that regard.

DATED as of the 2^nd day of April, 2009.

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EXERCISE FORM

TO: TRANSATLANTIC PETROLEUM CORP.

The undersigned holder of the within Warrants hereby exercises the right to acquire                      Common Shares without nominal or par value in the capital of TransAtlantic Petroleum Corp. at a price of US$1.20 per share (or such other number of other securities or property to which such Warrants entitle the undersigned in lieu thereof or in addition thereto) on the terms specified in the within Warrant Certificate and encloses and tenders herewith a certified cheque, bank draft or money order payable at par to or to the order of “TransAtlantic Petroleum Corp.” in lawful money of the United States for the aggregate subscription price of US$            .

The undersigned represents, warrants and certifies as follows (one of the following must be checked):

The undersigned holder understands that (i) the certificate representing the Common Shares will bear a legend restricting transfer without registration under the U.S. Securities Act and applicable state securities laws unless an exemption from registration is available and restricting hedging transactions unless in compliance with the U.S. Securities Act; and (ii) Common Shares will not be registered or delivered to an address in the United States unless box B is checked.

The undersigned hereby directs that the Common Shares hereby subscribed for be issued and delivered as follows:

OR

(Please state full names in which share certificates are to be issued, stating whether Mr., Mrs. or Miss)

DATED this      day of             ,             .

Instructions:

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TRANSFER FORM

FOR VALUE RECEIVED, the undersigned holder of the within Warrants hereby sells, assigns and transfers to                                         ,              Warrants of TransAtlantic Petroleum Corp. registered in the name of the undersigned on the records of the Corporation and irrevocably appoints                                          the attorney of the undersigned to transfer the said securities on the books or register with full power of substitution.

The undersigned hereby directs that the Warrants hereby transferred be issued and delivered as follows:

OR

(Please state full names in which share certificates are to be issued, stating whether Mr., Mrs. or Miss)

DATED this      day of                     ,         .

Instructions: