Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	7688m	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	61011968 = 211 · 313	Discriminant
Eigenvalues	2-  2  2 -4  6 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1312,18732]	[a1,a2,a3,a4,a6]
Generators	[1767:12340:27]	Generators of the group modulo torsion
j	4096766	j-invariant
L	6.010696715657	L(r)(E,1)/r!
Ω	1.9221502658963	Real period
R	6.2541382141673	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	15376o2 61504z2 69192p2 7688o2	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688m2

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	-4	6	-2	-4	-4	-8	6	-	-2	6	-6	12	-2	-12	2	4	0	-16	-4	-2	0	-14

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Quadratic twists for elliptic curve 7688m2

-4	8	-3	-31
15376o2	61504z2	69192p2	7688o2

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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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