Cremona's table of elliptic curves

12675 = 3 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Conductor	12675	Conductor
Count	8	Number of curves in isogeny class
Curves	12675e1 12675e2 12675e3 12675e4 12675e5 12675e6 12675e7 12675e8	Curves in isogeny class
deg	96768	Modular degree for the optimal curve
Eigenvalues	-1 3+ 5+  0 -4 13+ -2  4	Hecke eigenvalues for primes less than 20
L	2.0735704144974	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	38025bb 2535f 975a	Quadratic twists by: -3 5 13

Hecke Eigenvalues for isogeny class 12675e

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	+	+	0	-4	+	-2	4	-8	-2	8	6	6	4	-8	-6	12	-2	-4	0	-6	16	-4	-10	18

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Quadratic twists for isogeny class 12675e

-3	5	13
38025bb	2535f	975a

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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