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	696f	Isogeny class
Conductor	696	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-853419888 = -1 · 24 · 37 · 293	Discriminant
Eigenvalues	2- 3+ -2  3 -5  1 -7  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,56,-1415]	[a1,a2,a3,a4,a6]
Generators	[12:29:1]	Generators of the group modulo torsion
j	1192310528/53338743	j-invariant
L	1.8510015341829	L(r)(E,1)/r!
Ω	0.75879949851596	Real period
R	0.40656359987125	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	1392g1 5568j1 2088c1 17400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 696f1

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	3	-5	1	-7	2	4	-	-4	-12	-6	-8	3	-14	-2	-8	5	8	4	-2	14	15	14

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Quadratic twists for elliptic curve 696f1

-4	8	-3	5	-7	-11	13	29
1392g1	5568j1	2088c1	17400o1	34104y1	84216c1	117624i1	20184g1

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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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