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 (23 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
72.2-a8	\(\Q(\sqrt{-2}) \)	72.2	72.2-a	\( \bigl[a\) , \( 1\) , \( a\) , \( -95\) , \( 347\bigr] \)
144.2-a8	\(\Q(\sqrt{-2}) \)	144.2	144.2-a	\( \bigl[a\) , \( 0\) , \( a\) , \( -95\) , \( -346\bigr] \)
648.3-a8	\(\Q(\sqrt{-2}) \)	648.3	648.3-a	\( \bigl[a\) , \( -1\) , \( a\) , \( -863\) , \( -9355\bigr] \)
1296.3-b8	\(\Q(\sqrt{-2}) \)	1296.3	1296.3-b	\( \bigl[a\) , \( -1\) , \( 0\) , \( -864\) , \( 10220\bigr] \)
6912.2-a8	\(\Q(\sqrt{-2}) \)	6912.2	6912.2-a	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -768 a + 384\) , \( 2772 a - 13860\bigr] \)
6912.2-n8	\(\Q(\sqrt{-2}) \)	6912.2	6912.2-n	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -768 a + 384\) , \( -2772 a + 13860\bigr] \)
6912.3-a8	\(\Q(\sqrt{-2}) \)	6912.3	6912.3-a	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a + 384\) , \( -2772 a - 13860\bigr] \)
6912.3-n8	\(\Q(\sqrt{-2}) \)	6912.3	6912.3-n	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a + 384\) , \( 2772 a + 13860\bigr] \)
9216.2-m8	\(\Q(\sqrt{-2}) \)	9216.2	9216.2-m	\( \bigl[0\) , \( a\) , \( 0\) , \( 768\) , \( -5544 a\bigr] \)
9216.2-o8	\(\Q(\sqrt{-2}) \)	9216.2	9216.2-o	\( \bigl[0\) , \( -a\) , \( 0\) , \( 768\) , \( 5544 a\bigr] \)
20808.4-c8	\(\Q(\sqrt{-2}) \)	20808.4	20808.4-c	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1154 a - 96\) , \( -14320 a - 15496\bigr] \)
20808.6-c8	\(\Q(\sqrt{-2}) \)	20808.6	20808.6-c	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -1154 a - 96\) , \( 14320 a - 15496\bigr] \)
26136.4-d8	\(\Q(\sqrt{-2}) \)	26136.4	26136.4-d	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -769 a + 2979\) , \( -43172 a - 34454\bigr] \)
26136.6-i8	\(\Q(\sqrt{-2}) \)	26136.6	26136.6-i	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1922 a - 1634\) , \( -48352 a - 3366\bigr] \)
26136.7-i8	\(\Q(\sqrt{-2}) \)	26136.7	26136.7-i	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1922 a - 1634\) , \( 48352 a - 3366\bigr] \)
26136.9-d8	\(\Q(\sqrt{-2}) \)	26136.9	26136.9-d	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 769 a + 2979\) , \( 43172 a - 34454\bigr] \)
27648.2-v8	\(\Q(\sqrt{-2}) \)	27648.2	27648.2-v	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1538 a - 769\) , \( 29257 a + 10319\bigr] \)
27648.2-bb8	\(\Q(\sqrt{-2}) \)	27648.2	27648.2-bb	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1538 a - 769\) , \( -29257 a - 10319\bigr] \)
27648.3-f8	\(\Q(\sqrt{-2}) \)	27648.3	27648.3-f	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1538 a - 769\) , \( -29257 a + 10319\bigr] \)
27648.3-bp8	\(\Q(\sqrt{-2}) \)	27648.3	27648.3-bp	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 769\) , \( 29257 a - 10319\bigr] \)
41616.4-c8	\(\Q(\sqrt{-2}) \)	41616.4	41616.4-c	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 1152 a - 95\) , \( 13167 a + 15593\bigr] \)
41616.6-g8	\(\Q(\sqrt{-2}) \)	41616.6	41616.6-g	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1152 a - 95\) , \( -13167 a + 15593\bigr] \)
45000.2-i8	\(\Q(\sqrt{-2}) \)	45000.2	45000.2-i	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2402\) , \( 45714\bigr] \)