Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	7688i	Isogeny class
Conductor	7688	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	178560	Modular degree for the optimal curve
Δ	209824841467085056 = 28 · 3110	Discriminant
Eigenvalues	2-  1  3 -1 -1 -7  5  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4001924,3080010944]	[a1,a2,a3,a4,a6]
Generators	[1130:1418:1]	Generators of the group modulo torsion
j	33781072	j-invariant
L	5.4728877856403	L(r)(E,1)/r!
Ω	0.29450104181838	Real period
R	4.6458984931328	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	15376i1 61504s1 69192x1 7688e1	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688i1

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	-1	-1	-7	5	7	-8	-2	-	1	3	-7	0	9	-5	-2	-7	5	-3	1	3	-6	-10

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Quadratic twists for elliptic curve 7688i1

-4	8	-3	-31
15376i1	61504s1	69192x1	7688e1

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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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