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-a2	\(\Q(\zeta_{21})^+\)	27	27.1	27.1-a	\( \bigl[0\) , \( -a^{5} + 4 a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{4} - 3 a^{2} + 1\) , \( -2 a^{5} + 7 a^{4} + 4 a^{3} - 28 a^{2} + 17 a + 4\) , \( -6 a^{5} + 13 a^{4} + 15 a^{3} - 52 a^{2} + 33 a - 3\bigr] \)
27.1-b2	\(\Q(\zeta_{21})^+\)	27	27.1	27.1-b	\( \bigl[0\) , \( -a^{5} + 5 a^{3} - a^{2} - 5 a + 2\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{5} + 7 a^{3} - a^{2} - 11 a + 2\) , \( a^{5} - 7 a^{3} + a^{2} + 11 a - 2\bigr] \)