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	696d	Isogeny class
Conductor	696	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-12137527296 = -1 · 211 · 35 · 293	Discriminant
Eigenvalues	2- 3+  1 -3 -2  4  5  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5920,177388]	[a1,a2,a3,a4,a6]
j	-11205525764162/5926527	j-invariant
L	1.251911252575	L(r)(E,1)/r!
Ω	1.251911252575	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1392e1 5568n1 2088e1 17400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 696d1

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	-3	-2	4	5	5	4	+	8	-3	9	-5	3	10	7	10	8	-4	-14	-14	8	6	-16

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Quadratic twists for elliptic curve 696d1

-4	8	-3	5	-7	-11	13	29
1392e1	5568n1	2088e1	17400j1	34104w1	84216f1	117624b1	20184e1

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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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