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	Bad primes

  *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 (13 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
75.1-a8	\(\Q(\sqrt{-3}) \)	75.1	75.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
1875.1-b8	\(\Q(\sqrt{-3}) \)	1875.1	1875.1-b	\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)
11025.1-c8	\(\Q(\sqrt{-3}) \)	11025.1	11025.1-c	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 32400 a + 19440\) , \( -2333509 a + 4285239\bigr] \)
11025.3-c8	\(\Q(\sqrt{-3}) \)	11025.3	11025.3-c	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -19438 a - 32401\) , \( 2281669 a + 1971170\bigr] \)
12675.1-a8	\(\Q(\sqrt{-3}) \)	12675.1	12675.1-a	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -17279 a + 32400\) , \( -1393193 a - 637617\bigr] \)
12675.3-a8	\(\Q(\sqrt{-3}) \)	12675.3	12675.3-a	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -32400 a + 17281\) , \( 1408313 a - 2063210\bigr] \)
19200.1-g8	\(\Q(\sqrt{-3}) \)	19200.1	19200.1-g	\( \bigl[0\) , \( 1\) , \( 0\) , \( -34560\) , \( 2461428\bigr] \)
57600.1-j8	\(\Q(\sqrt{-3}) \)	57600.1	57600.1-j	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -103680 a\) , \( -14768568 a + 7384284\bigr] \)
57600.1-k8	\(\Q(\sqrt{-3}) \)	57600.1	57600.1-k	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 103682 a - 103681\) , \( 14872249 a - 7487965\bigr] \)
81225.1-a8	\(\Q(\sqrt{-3}) \)	81225.1	81225.1-a	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -32401 a - 103681\) , \( -6545490 a - 12381240\bigr] \)
81225.3-a8	\(\Q(\sqrt{-3}) \)	81225.3	81225.3-a	\( \bigl[1\) , \( a\) , \( a\) , \( 103681 a + 32400\) , \( 6545489 a - 18926729\bigr] \)
102675.1-a8	\(\Q(\sqrt{-3}) \)	102675.1	102675.1-a	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 15120 a + 71281\) , \( 9735073 a - 6968786\bigr] \)
102675.3-a8	\(\Q(\sqrt{-3}) \)	102675.3	102675.3-a	\( \bigl[1\) , \( -a\) , \( 0\) , \( 86401 a - 71281\) , \( -9735073 a + 2766287\bigr] \)