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	6475d	Isogeny class
Conductor	6475	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-467919921875 = -1 · 511 · 7 · 372	Discriminant
Eigenvalues	2 -1 5+ 7-  1  1  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1758,44043]	[a1,a2,a3,a4,a6]
j	-38477541376/29946875	j-invariant
L	3.436227197382	L(r)(E,1)/r!
Ω	0.85905679934549	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	103600ba1 58275w1 1295b1 45325g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6475d1

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	-1	+	-	1	1	3	4	4	-3	-4	+	-4	8	3	-6	10	-12	10	0	-2	5	0	8	11

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Quadratic twists for elliptic curve 6475d1

-4	-3	5	-7
103600ba1	58275w1	1295b1	45325g1

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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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