Cremona's table of elliptic curves

69696 = 2⁶ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	69696gl	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	81920	Modular degree for the optimal curve
Δ	-3967389600768 = -1 · 210 · 37 · 116	Discriminant
Eigenvalues	2- 3- -2  0 11- -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2904,-74536]	[a1,a2,a3,a4,a6]
Generators	[25:117:1] [34:252:1]	Generators of the group modulo torsion
j	2048/3	j-invariant
L	9.5908735714278	L(r)(E,1)/r!
Ω	0.41500304918564	Real period
R	5.7775922310936	Regulator
r	2	Rank of the group of rational points
S	1.0000000000008	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696cp1 17424t1 23232cz1 576i1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696gl1

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	0	-	-2	2	4	-8	-6	-8	-6	-6	-4	0	-2	-4	-2	-4	8	-10	-8	-4	6	2

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Quadratic twists for elliptic curve 69696gl1

-4	8	-3	-11
69696cp1	17424t1	23232cz1	576i1

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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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