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	11616b	Isogeny class
Conductor	11616	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-4460544 = -1 · 212 · 32 · 112	Discriminant
Eigenvalues	2+ 3+ -1 -2 11- -1 -5 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-161,849]	[a1,a2,a3,a4,a6]
Generators	[-3:36:1] [5:12:1]	Generators of the group modulo torsion
j	-937024/9	j-invariant
L	5.0920396101575	L(r)(E,1)/r!
Ω	2.4632618540175	Real period
R	0.25839922387125	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11616y1 23232bs1 34848bu1 11616r1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 11616b1

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	-2	-	-1	-5	-8	-6	-3	-4	-11	3	2	-4	3	-6	10	2	-6	2	0	-12	13	-9

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Quadratic twists for elliptic curve 11616b1

-4	8	-3	-11
11616y1	23232bs1	34848bu1	11616r1

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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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