Cremona's table of elliptic curves

7688 = 2³ · 31²

Field	Data	Notes
Atkin-Lehner	2+ 31-	Signs for the Atkin-Lehner involutions
Class	7688b	Isogeny class
Conductor	7688	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	74400	Modular degree for the optimal curve
Δ	839299365868340224 = 210 · 3110	Discriminant
Eigenvalues	2+ -1  1  3  5 -1 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-307840,48878204]	[a1,a2,a3,a4,a6]
j	3844	j-invariant
L	2.1088441792798	L(r)(E,1)/r!
Ω	0.26360552240997	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15376g1 61504o1 69192bh1 7688a1	Quadratic twists by: -4 8 -3 -31

Hecke Eigenvalues for elliptic curve 7688b1

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	1	3	5	-1	-3	1	0	2	-	11	-5	11	-4	-5	-3	-6	3	9	13	-3	1	10	2

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Quadratic twists for elliptic curve 7688b1

-4	8	-3	-31
15376g1	61504o1	69192bh1	7688a1

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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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