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	696c	Isogeny class
Conductor	696	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-112752 = -1 · 24 · 35 · 29	Discriminant
Eigenvalues	2+ 3-  0 -5 -5  1 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,12,9]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	10976000/7047	j-invariant
L	2.2838622912177	L(r)(E,1)/r!
Ω	2.076311058055	Real period
R	0.10999615314658	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	1392c1 5568a1 2088j1 17400bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 696c1

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
+	-	0	-5	-5	1	-3	-4	2	-	2	2	-6	-8	7	12	6	-6	-15	2	-10	-4	-6	3	8

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Quadratic twists for elliptic curve 696c1

-4	8	-3	5	-7	-11	13	29
1392c1	5568a1	2088j1	17400bf1	34104i1	84216s1	117624bx1	20184m1

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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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