Cremona's table of elliptic curves

11616 = 2⁵ · 3 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	11616v	Isogeny class
Conductor	11616	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-1486848 = -1 · 212 · 3 · 112	Discriminant
Eigenvalues	2- 3+ -2 -3 11- -6  4  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29,-75]	[a1,a2,a3,a4,a6]
Generators	[7:4:1]	Generators of the group modulo torsion
j	-5632/3	j-invariant
L	2.5363068302193	L(r)(E,1)/r!
Ω	1.0007487484079	Real period
R	1.2672045976847	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	11616n1 23232bz1 34848x1 11616f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 11616v1

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	-3	-	-6	4	5	-2	-2	1	7	-4	-4	-8	6	6	9	13	10	11	-13	4	-14	-7

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Quadratic twists for elliptic curve 11616v1

-4	8	-3	-11
11616n1	23232bz1	34848x1	11616f1

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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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