Cremona's table of elliptic curves

12584 = 2³ · 11² · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	12584k	Isogeny class
Conductor	12584	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	42240	Modular degree for the optimal curve
Δ	1273439232050128 = 24 · 118 · 135	Discriminant
Eigenvalues	2- -1  0  4 11- 13+ -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-48803,3794188]	[a1,a2,a3,a4,a6]
Generators	[81:605:1]	Generators of the group modulo torsion
j	3748096000/371293	j-invariant
L	4.3232547874727	L(r)(E,1)/r!
Ω	0.47028128278143	Real period
R	1.5321521203592	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	25168a1 100672be1 113256l1 12584f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 12584k1

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	0	4	-	+	-1	4	3	1	2	-8	-8	-11	4	3	0	-1	2	6	-8	-5	4	-14	-2

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Quadratic twists for elliptic curve 12584k1

-4	8	-3	-11
25168a1	100672be1	113256l1	12584f1

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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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