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	11616h	Isogeny class
Conductor	11616	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	3741536832 = 26 · 3 · 117	Discriminant
Eigenvalues	2+ 3+ -4 -2 11- -4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1250,-16344]	[a1,a2,a3,a4,a6]
Generators	[-20:16:1] [70:484:1]	Generators of the group modulo torsion
j	1906624/33	j-invariant
L	4.3552513170916	L(r)(E,1)/r!
Ω	0.80370956103754	Real period
R	2.7094684001696	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11616bf1 23232ck1 34848ck1 1056h1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 11616h1

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
+	+	-4	-2	-	-4	-2	4	-6	6	-4	-2	-6	8	-10	-12	0	-8	-4	-6	-10	-6	-12	-14	-18

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Quadratic twists for elliptic curve 11616h1

-4	8	-3	-11
11616bf1	23232ck1	34848ck1	1056h1

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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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