Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	7688a	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	945685504 = 210 · 314	Discriminant
Eigenvalues	2+  1  1  3 -5  1  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-320,-1744]	[a1,a2,a3,a4,a6]
Generators	[20:16:1]	Generators of the group modulo torsion
j	3844	j-invariant
L	5.4360089829732	L(r)(E,1)/r!
Ω	1.1502489020044	Real period
R	2.3629707333345	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	15376c1 61504f1 69192bd1 7688b1	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688a1

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
+	1	1	3	-5	1	3	1	0	-2	+	-11	-5	-11	-4	5	-3	6	3	9	-13	3	-1	-10	2

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Quadratic twists for elliptic curve 7688a1

-4	8	-3	-31
15376c1	61504f1	69192bd1	7688b1

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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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