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