Cremona's table of elliptic curves

10656 = 2⁵ · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	10656m	Isogeny class
Conductor	10656	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1792	Modular degree for the optimal curve
Δ	-41430528 = -1 · 29 · 37 · 37	Discriminant
Eigenvalues	2- 3-  0  3 -3  5 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,-398]	[a1,a2,a3,a4,a6]
Generators	[14:36:1]	Generators of the group modulo torsion
j	-125000/111	j-invariant
L	5.0085917584941	L(r)(E,1)/r!
Ω	0.78221425715975	Real period
R	1.6007736092284	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	10656n1 21312cb1 3552c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10656m1

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	3	-3	5	-3	-1	-1	0	2	+	-10	-4	6	3	-8	-6	2	8	-11	-14	-11	5	-2

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Quadratic twists for elliptic curve 10656m1

-4	8	-3
10656n1	21312cb1	3552c1

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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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