Elliptic Curve Search Results

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Base field	Conductor norm	Isogenous curves	Base change curves	\(\Q\)-curves	CM curves
Torsion order	Isogeny degree	Torsion structure	j-invariant

Results (displaying both matches)

Label	Base field	Conductor norm	Conductor label	Isogeny class	Weierstrass coefficients
27.1-a1	\(\Q(\zeta_{21})^+\)	27	27.1	27.1-a	\( \bigl[0\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( a^{3} - 2 a\) , \( 652 a^{5} + 912 a^{4} - 2478 a^{3} - 3387 a^{2} + 131 a - 130\) , \( -26388 a^{5} - 27297 a^{4} + 115694 a^{3} + 96838 a^{2} - 65135 a + 8321\bigr] \)
27.1-b1	\(\Q(\zeta_{21})^+\)	27	27.1	27.1-b	\( \bigl[0\) , \( -a^{5} + 5 a^{3} - a^{2} - 5 a + 2\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -391 a^{5} + 2607 a^{3} - 391 a^{2} - 3911 a + 522\) , \( -5979 a^{5} + 40423 a^{3} - 5979 a^{2} - 61479 a + 8968\bigr] \)