Cremona's table of elliptic curves

9696 = 2⁵ · 3 · 101

Field	Data	Notes
Atkin-Lehner	2- 3- 101+	Signs for the Atkin-Lehner involutions
Class	9696i	Isogeny class
Conductor	9696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	3723264 = 212 · 32 · 101	Discriminant
Eigenvalues	2- 3- -3  0  4 -3 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-77,219]	[a1,a2,a3,a4,a6]
Generators	[1:12:1]	Generators of the group modulo torsion
j	12487168/909	j-invariant
L	4.4286413475432	L(r)(E,1)/r!
Ω	2.4378953902667	Real period
R	0.4541459577413	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	9696e1 19392bd1 29088i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 9696i1

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
-	-	-3	0	4	-3	-3	1	1	0	5	-2	-4	4	-1	0	0	-14	14	-3	-14	5	4	18	-10

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Quadratic twists for elliptic curve 9696i1

-4	8	-3
9696e1	19392bd1	29088i1

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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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