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 (9 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
588.2-a5	\(\Q(\sqrt{-3}) \)	588.2	588.2-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
12348.2-b5	\(\Q(\sqrt{-3}) \)	12348.2	12348.2-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1260 a + 756\) , \( 17183 a - 33024\bigr] \)
12348.3-b5	\(\Q(\sqrt{-3}) \)	12348.3	12348.3-b	\( \bigl[a\) , \( -1\) , \( 1\) , \( -1261 a + 2017\) , \( -17183 a - 15841\bigr] \)
28812.3-f5	\(\Q(\sqrt{-3}) \)	28812.3	28812.3-f	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4117 a + 4117\) , \( -101935\bigr] \)
37632.2-r5	\(\Q(\sqrt{-3}) \)	37632.2	37632.2-r	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1344\) , \( -19404\bigr] \)
99372.4-g5	\(\Q(\sqrt{-3}) \)	99372.4	99372.4-g	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -671 a + 1260\) , \( 10579 a + 5784\bigr] \)
99372.6-h5	\(\Q(\sqrt{-3}) \)	99372.6	99372.6-h	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1260 a + 673\) , \( -9991 a + 15103\bigr] \)
112896.2-k5	\(\Q(\sqrt{-3}) \)	112896.2	112896.2-k	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4033\) , \( -112391 a + 58212\bigr] \)
112896.2-u5	\(\Q(\sqrt{-3}) \)	112896.2	112896.2-u	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4032 a\) , \( 116424 a - 58212\bigr] \)