Cremona's table of elliptic curves

696 = 2³ · 3 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 29+	Signs for the Atkin-Lehner involutions
Class	696g	Isogeny class
Conductor	696	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-12528 = -1 · 24 · 33 · 29	Discriminant
Eigenvalues	2- 3- -2 -1 -3 -7  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4,5]	[a1,a2,a3,a4,a6]
Generators	[2:-3:1]	Generators of the group modulo torsion
j	-562432/783	j-invariant
L	2.2393010520501	L(r)(E,1)/r!
Ω	3.6032980856372	Real period
R	0.10357645499716	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	1392a1 5568d1 2088f1 17400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 696g1

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	-1	-3	-7	3	-6	4	+	0	-8	6	4	-3	-10	10	0	9	-12	-4	10	6	-3	-10

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Quadratic twists for elliptic curve 696g1

-4	8	-3	5	-7	-11	13	29
1392a1	5568d1	2088f1	17400a1	34104v1	84216j1	117624m1	20184a1

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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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