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	6475c	Isogeny class
Conductor	6475	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-17705078125 = -1 · 510 · 72 · 37	Discriminant
Eigenvalues	-1  2 5+ 7- -2  4 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,612,2906]	[a1,a2,a3,a4,a6]
j	2595575/1813	j-invariant
L	1.5552572298268	L(r)(E,1)/r!
Ω	0.77762861491341	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	103600bh1 58275p1 6475f1 45325f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6475c1

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	2	+	-	-2	4	-6	-5	-5	6	8	+	5	-1	0	9	1	-12	10	12	7	5	18	2	8

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Quadratic twists for elliptic curve 6475c1

-4	-3	5	-7
103600bh1	58275p1	6475f1	45325f1

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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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