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
15.2-a2	\(\Q(\sqrt{21}) \)	15.2	15.2-a	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 0\) , \( 3 a - 10\bigr] \)
15.2-b2	\(\Q(\sqrt{21}) \)	15.2	15.2-b	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
45.1-a2	\(\Q(\sqrt{21}) \)	45.1	45.1-a	\( \bigl[1\) , \( a\) , \( 1\) , \( a + 2\) , \( -2 a - 4\bigr] \)
45.1-b2	\(\Q(\sqrt{21}) \)	45.1	45.1-b	\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 2\) , \( -a + 7\bigr] \)
1875.1-e2	\(\Q(\sqrt{21}) \)	1875.1	1875.1-e	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( a - 2\) , \( -10 a + 1\bigr] \)
1875.1-bp2	\(\Q(\sqrt{21}) \)	1875.1	1875.1-bp	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17 a - 45\) , \( 456 a - 1278\bigr] \)