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
Δ	-3442688 = -1 · 211 · 412	Discriminant
Eigenvalues	2+  0 -2  2  0 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,29,66]	[a1,a2,a3,a4,a6]
Generators	[-1:6:1]	Generators of the group modulo torsion
j	1317006/1681	j-invariant
L	2.0060295838619	L(r)(E,1)/r!
Ω	1.6828879541039	Real period
R	1.1920161285663	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	328a2 2624d2 5904h2 16400b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 656a2

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 656a2

-4	8	-3	5	-7	-11	13	41
328a2	2624d2	5904h2	16400b2	32144f2	79376j2	110864d2	26896a2

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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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