Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31+	Signs for the Atkin-Lehner involutions
Class	7688f	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	44640	Modular degree for the optimal curve
Δ	873360422339584 = 210 · 318	Discriminant
Eigenvalues	2- -1 -3  5  1  1 -5 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69512,6932476]	[a1,a2,a3,a4,a6]
j	42532	j-invariant
L	0.9972592976573	L(r)(E,1)/r!
Ω	0.49862964882865	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15376b1 61504b1 69192f1 7688j1	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688f1

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 7688f1

-4	8	-3	-31
15376b1	61504b1	69192f1	7688j1

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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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