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-a3	\(\Q(\sqrt{21}) \)	15.2	15.2-a	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -64 a - 116\) , \( -387 a - 694\bigr] \)
15.2-b3	\(\Q(\sqrt{21}) \)	15.2	15.2-b	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 55\) , \( -57 a + 152\bigr] \)
45.1-a3	\(\Q(\sqrt{21}) \)	45.1	45.1-a	\( \bigl[1\) , \( a\) , \( 1\) , \( -29 a - 103\) , \( 136 a + 128\bigr] \)
45.1-b3	\(\Q(\sqrt{21}) \)	45.1	45.1-b	\( \bigl[a\) , \( a\) , \( 0\) , \( 257 a - 718\) , \( -3487 a + 9718\bigr] \)
1875.1-e3	\(\Q(\sqrt{21}) \)	1875.1	1875.1-e	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 376 a - 1377\) , \( -7635 a + 22626\bigr] \)
1875.1-bp3	\(\Q(\sqrt{21}) \)	1875.1	1875.1-bp	\( \bigl[a\) , \( 0\) , \( 1\) , \( -1606 a - 2965\) , \( -39293 a - 70734\bigr] \)