Cremona's table of elliptic curves

12675 = 3 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	12675n	Isogeny class
Conductor	12675	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	179712	Modular degree for the optimal curve
Δ	-8603409948046875 = -1 · 33 · 58 · 138	Discriminant
Eigenvalues	-2 3+ 5+ -5  2 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-128158,18256968]	[a1,a2,a3,a4,a6]
Generators	[282:-2113:1]	Generators of the group modulo torsion
j	-18264064/675	j-invariant
L	1.3131521792997	L(r)(E,1)/r!
Ω	0.41004159175956	Real period
R	0.53374755378058	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38025bo1 2535g1 12675l1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 12675n1

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
-2	+	+	-5	2	+	-2	0	-6	-4	-7	2	6	-1	8	4	12	-13	7	12	-15	3	-8	14	5

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Quadratic twists for elliptic curve 12675n1

-3	5	13
38025bo1	2535g1	12675l1

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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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