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-a2	\(\Q(\sqrt{21}) \)	15.1	15.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 174 a + 260\) , \( 145 a + 374\bigr] \)
15.1-b2	\(\Q(\sqrt{21}) \)	15.1	15.1-b	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 275 a - 734\) , \( 3747 a - 10492\bigr] \)
45.2-a2	\(\Q(\sqrt{21}) \)	45.2	45.2-a	\( \bigl[a\) , \( a\) , \( 0\) , \( 2347 a + 4171\) , \( 20528 a + 36708\bigr] \)
45.2-b2	\(\Q(\sqrt{21}) \)	45.2	45.2-b	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 273 a - 279\) , \( -1724 a + 5275\bigr] \)
1875.1-k2	\(\Q(\sqrt{21}) \)	1875.1	1875.1-k	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4359 a + 6472\) , \( 39901 a + 90526\bigr] \)
1875.1-bj2	\(\Q(\sqrt{21}) \)	1875.1	1875.1-bj	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 6872 a - 18375\) , \( 456884 a - 1277134\bigr] \)