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	5656c	Isogeny class
Conductor	5656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-723968 = -1 · 210 · 7 · 101	Discriminant
Eigenvalues	2+ -1 -2 7-  6 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,16,28]	[a1,a2,a3,a4,a6]
Generators	[2:8:1]	Generators of the group modulo torsion
j	415292/707	j-invariant
L	2.9433510891666	L(r)(E,1)/r!
Ω	1.9527063094368	Real period
R	0.7536594404756	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	11312c1 45248j1 50904j1 39592a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5656c1

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	-	6	-2	-4	0	9	-8	-4	-3	6	-1	0	-6	-3	9	14	13	-3	-1	7	-15	10

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Quadratic twists for elliptic curve 5656c1

-4	8	-3	-7
11312c1	45248j1	50904j1	39592a1

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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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