Cremona's table of elliptic curves

11696 = 2⁴ · 17 · 43

Field	Data	Notes
Atkin-Lehner	2- 17+ 43-	Signs for the Atkin-Lehner involutions
Class	11696l	Isogeny class
Conductor	11696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-865316864 = -1 · 212 · 173 · 43	Discriminant
Eigenvalues	2- -1 -1  0  6  1 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8616,-304976]	[a1,a2,a3,a4,a6]
Generators	[108:112:1]	Generators of the group modulo torsion
j	-17271547035049/211259	j-invariant
L	3.6636566748922	L(r)(E,1)/r!
Ω	0.24776423590417	Real period
R	3.6967166200586	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	731a1 46784t1 105264bw1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11696l1

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	-1	0	6	1	+	2	-2	6	-2	-3	-4	-	-13	1	3	-7	9	-11	-7	8	9	2	10

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Quadratic twists for elliptic curve 11696l1

-4	8	-3
731a1	46784t1	105264bw1

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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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