Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	7688o	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	54148346185054208 = 211 · 319	Discriminant
Eigenvalues	2- -2  2 -4 -6  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1261152,-545434592]	[a1,a2,a3,a4,a6]
Generators	[5335967168330259537701:101236988063103181027180:3630812325786441739]	Generators of the group modulo torsion
j	4096766	j-invariant
L	2.5750205792269	L(r)(E,1)/r!
Ω	0.14246691800061	Real period
R	36.149031864589	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	15376k2 61504u2 69192o2 7688m2	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688o2

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 7688o2

-4	8	-3	-31
15376k2	61504u2	69192o2	7688m2

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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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