Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	7688j	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	984064 = 210 · 312	Discriminant
Eigenvalues	2-  1 -3  5 -1 -1  5 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-72,-256]	[a1,a2,a3,a4,a6]
Generators	[-5:2:1]	Generators of the group modulo torsion
j	42532	j-invariant
L	4.6087016561949	L(r)(E,1)/r!
Ω	1.6394075203235	Real period
R	1.4055997667027	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	15376j1 61504r1 69192u1 7688f1	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688j1

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	-3	5	-1	-1	5	-5	4	-2	-	-5	-9	5	0	-9	7	-14	-7	-1	-15	7	15	18	-10

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Quadratic twists for elliptic curve 7688j1

-4	8	-3	-31
15376j1	61504r1	69192u1	7688f1

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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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