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	11616s	Isogeny class
Conductor	11616	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-131153375232 = -1 · 212 · 37 · 114	Discriminant
Eigenvalues	2- 3+  2 -1 11- -2 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,323,17173]	[a1,a2,a3,a4,a6]
Generators	[-9:116:1]	Generators of the group modulo torsion
j	61952/2187	j-invariant
L	4.1902811822234	L(r)(E,1)/r!
Ω	0.78556492868798	Real period
R	2.6670495519841	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	11616l1 23232cd1 34848z1 11616c1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 11616s1

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	-1	-	-2	-4	-1	6	-6	5	7	0	4	-4	6	6	-1	-7	6	-11	9	0	-2	9

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Quadratic twists for elliptic curve 11616s1

-4	8	-3	-11
11616l1	23232cd1	34848z1	11616c1

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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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