Cremona's table of elliptic curves

656 = 2⁴ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41-	Signs for the Atkin-Lehner involutions
Class	656b	Isogeny class
Conductor	656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	10496 = 28 · 41	Discriminant
Eigenvalues	2+ -2  2  2 -2  6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12,-20]	[a1,a2,a3,a4,a6]
j	810448/41	j-invariant
L	1.2777975495193	L(r)(E,1)/r!
Ω	2.5555950990386	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	328b1 2624h1 5904e1 16400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 656b1

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	2	2	-2	6	-6	2	0	6	8	10	-	0	6	-2	4	-2	10	2	-2	2	-12	10	-6

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Quadratic twists for elliptic curve 656b1

-4	8	-3	5	-7	-11	13	41
328b1	2624h1	5904e1	16400j1	32144d1	79376g1	110864c1	26896b1

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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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