Cremona's table of elliptic curves

656 = 2⁴ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	656a	Isogeny class
Conductor	656	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	41984 = 210 · 41	Discriminant
Eigenvalues	2+  0 -2  2  0 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11,10]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1]	Generators of the group modulo torsion
j	143748/41	j-invariant
L	2.0060295838619	L(r)(E,1)/r!
Ω	3.3657759082078	Real period
R	0.59600806428317	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	328a1 2624d1 5904h1 16400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 656a1

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	-2	2	0	-4	-2	-4	4	0	-4	-6	+	-12	6	-4	4	10	-12	6	-2	2	4	-6	14

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Quadratic twists for elliptic curve 656a1

-4	8	-3	5	-7	-11	13	41
328a1	2624d1	5904h1	16400b1	32144f1	79376j1	110864d1	26896a1

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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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