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	5.5.36497.1	27	27.1	27.1-a	\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{2} + 3\) , \( -1\bigr] \)
27.1-b1	5.5.36497.1	27	27.1	27.1-b	\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - a + 1\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -5 a^{4} + 6 a^{3} + 16 a^{2} - 9 a - 5\) , \( -3 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 3\bigr] \)