Cremona's table of elliptic curves

6475 = 5² · 7 · 37

Field	Data	Notes
Atkin-Lehner	5- 7- 37-	Signs for the Atkin-Lehner involutions
Class	6475g	Isogeny class
Conductor	6475	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-58695875 = -1 · 53 · 73 · 372	Discriminant
Eigenvalues	0 -3 5- 7- -3 -5 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-40,381]	[a1,a2,a3,a4,a6]
Generators	[1:18:1] [5:17:1]	Generators of the group modulo torsion
j	-56623104/469567	j-invariant
L	3.0257282649731	L(r)(E,1)/r!
Ω	1.6940319090682	Real period
R	0.14884254584077	Regulator
r	2	Rank of the group of rational points
S	0.99999999999948	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	103600ca1 58275bi1 6475e1 45325s1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6475g1

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
0	-3	-	-	-3	-5	-3	-6	-4	9	-10	-	2	-2	-7	4	-12	12	-8	-12	-14	13	-12	-12	-11

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Quadratic twists for elliptic curve 6475g1

-4	-3	5	-7
103600ca1	58275bi1	6475e1	45325s1

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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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