Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree	Base change curves	\(\Q\)-curves	Torsion structure	CM
Analytic order* of Ш	Cyclic isogeny degree	Isogeny class size	Semistable	j-invariant
Regulator*	Curves per isogeny class	Isogeny class degree	Potential good reduction

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.

Results (8 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
72.1-c6	\(\Q(\sqrt{7}) \)	72.1	72.1-c	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4610 a - 12196\) , \( -286494 a - 757992\bigr] \)
72.1-d6	\(\Q(\sqrt{7}) \)	72.1	72.1-d	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4611 a - 12197\) , \( 269682 a + 713511\bigr] \)
432.1-c6	\(\Q(\sqrt{7}) \)	432.1	432.1-c	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 383 a - 1060\) , \( -6584 a + 17323\bigr] \)
432.1-g6	\(\Q(\sqrt{7}) \)	432.1	432.1-g	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 385 a - 1055\) , \( 6968 a - 18381\bigr] \)
432.2-c6	\(\Q(\sqrt{7}) \)	432.2	432.2-c	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -385 a - 1060\) , \( 6583 a + 17323\bigr] \)
432.2-g6	\(\Q(\sqrt{7}) \)	432.2	432.2-g	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -385 a - 1055\) , \( -6968 a - 18381\bigr] \)
648.1-f6	\(\Q(\sqrt{7}) \)	648.1	648.1-f	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -41505 a - 109815\) , \( -7584046 a - 20065501\bigr] \)
648.1-m6	\(\Q(\sqrt{7}) \)	648.1	648.1-m	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -41506 a - 109819\) , \( 7391211 a + 19555309\bigr] \)