Cremona's table of elliptic curves

7656 = 2³ · 3 · 11 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 29+	Signs for the Atkin-Lehner involutions
Class	7656g	Isogeny class
Conductor	7656	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	575486208 = 28 · 35 · 11 · 292	Discriminant
Eigenvalues	2- 3-  2  2 11+ -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-852,-9792]	[a1,a2,a3,a4,a6]
Generators	[-18:6:1]	Generators of the group modulo torsion
j	267492843088/2247993	j-invariant
L	5.7578490772448	L(r)(E,1)/r!
Ω	0.88403070113513	Real period
R	0.65131777322343	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	15312e1 61248m1 22968k1 84216i1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7656g1

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

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Quadratic twists for elliptic curve 7656g1

-4	8	-3	-11
15312e1	61248m1	22968k1	84216i1

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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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