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
2.2-a7	3.3.316.1	2.2	2.2-a	\( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 3795999062 a^{2} - 2009285242 a - 16129733497\) , \( 186167522763990 a^{2} - 98541556480493 a - 791051967859626\bigr] \)
16.5-b4	3.3.316.1	16.5	16.5-b	\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( 0\) , \( 297980666 a^{2} - 157726108 a - 1266161726\) , \( -4093950113647 a^{2} + 2166995673374 a + 17395769388977\bigr] \)
32.1-c5	3.3.316.1	32.1	32.1-c	\( \bigl[a\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 486273921 a^{2} - 257393114 a - 2066246710\) , \( -8535646743838 a^{2} + 4518059339552 a + 36269162590988\bigr] \)
64.7-a6	3.3.316.1	64.7	64.7-a	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a + 1\) , \( 7908272 a^{2} - 4185996 a - 33603389\) , \( 17708327376 a^{2} - 9373311330 a - 75245171795\bigr] \)
64.7-d1	3.3.316.1	64.7	64.7-d	\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 7908273 a^{2} - 4185996 a - 33603392\) , \( -17708327376 a^{2} + 9373311329 a + 75245171793\bigr] \)
242.3-b2	3.3.316.1	242.3	242.3-b	\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a\) , \( 163201859571 a^{2} - 86385450180 a - 693467637401\) , \( 52479892685555807 a^{2} - 27778477321846893 a - 222994439446883602\bigr] \)