Cremona's table of elliptic curves

5656 = 2³ · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 7+ 101-	Signs for the Atkin-Lehner involutions
Class	5656b	Isogeny class
Conductor	5656	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	1266944 = 28 · 72 · 101	Discriminant
Eigenvalues	2+ -2 -3 7+  0 -1 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-57,139]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1] [-1:14:1]	Generators of the group modulo torsion
j	81415168/4949	j-invariant
L	3.3149103051784	L(r)(E,1)/r!
Ω	2.6778778787203	Real period
R	0.15473587927218	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11312h1 45248c1 50904h1 39592d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5656b1

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	-3	+	0	-1	-3	-1	-5	-4	-5	-6	0	-8	-13	12	2	-10	-8	3	-14	9	-14	-16	-18

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Quadratic twists for elliptic curve 5656b1

-4	8	-3	-7
11312h1	45248c1	50904h1	39592d1

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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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