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-a4	\(\Q(\sqrt{-3}) \)	588.2	588.2-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
12348.2-b4	\(\Q(\sqrt{-3}) \)	12348.2	12348.2-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 13710 a + 8226\) , \( -638437 a + 1167672\bigr] \)
12348.3-b4	\(\Q(\sqrt{-3}) \)	12348.3	12348.3-b	\( \bigl[a\) , \( -1\) , \( 1\) , \( -13711 a + 21937\) , \( 638437 a + 529235\bigr] \)
28812.3-f4	\(\Q(\sqrt{-3}) \)	28812.3	28812.3-f	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44787 a + 44787\) , \( 3609423\bigr] \)
37632.2-r4	\(\Q(\sqrt{-3}) \)	37632.2	37632.2-r	\( \bigl[0\) , \( 1\) , \( 0\) , \( -14624\) , \( 669300\bigr] \)
99372.4-g4	\(\Q(\sqrt{-3}) \)	99372.4	99372.4-g	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7311 a + 13710\) , \( -380137 a - 170928\bigr] \)
99372.6-h4	\(\Q(\sqrt{-3}) \)	99372.6	99372.6-h	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13710 a + 7313\) , \( 386535 a - 564775\bigr] \)
112896.2-k4	\(\Q(\sqrt{-3}) \)	112896.2	112896.2-k	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 43873\) , \( 4059673 a - 2007900\bigr] \)
112896.2-u4	\(\Q(\sqrt{-3}) \)	112896.2	112896.2-u	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -43872 a\) , \( -4015800 a + 2007900\bigr] \)