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 (6 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
15.1-a1	\(\Q(\sqrt{21}) \)	15.1	15.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -4 a - 7\bigr] \)
15.1-b1	\(\Q(\sqrt{21}) \)	15.1	15.1-b	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
45.2-a1	\(\Q(\sqrt{21}) \)	45.2	45.2-a	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( 2 a - 6\bigr] \)
45.2-b1	\(\Q(\sqrt{21}) \)	45.2	45.2-b	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 6\) , \( 4 a + 7\bigr] \)
1875.1-k1	\(\Q(\sqrt{21}) \)	1875.1	1875.1-k	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -16 a - 28\) , \( -474 a - 849\bigr] \)
1875.1-bj1	\(\Q(\sqrt{21}) \)	1875.1	1875.1-bj	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3 a\) , \( 9 a - 9\bigr] \)