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	12584m	Isogeny class
Conductor	12584	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	402688 = 28 · 112 · 13	Discriminant
Eigenvalues	2- -3  0  0 11- 13- -7 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-55,154]	[a1,a2,a3,a4,a6]
Generators	[-2:16:1] [1:10:1]	Generators of the group modulo torsion
j	594000/13	j-invariant
L	4.3469796795174	L(r)(E,1)/r!
Ω	2.9931287136156	Real period
R	0.36307991531926	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25168l1 100672x1 113256v1 12584a1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 12584m1

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
-	-3	0	0	-	-	-7	-4	-7	-9	-6	-8	-12	1	12	3	12	-15	-10	6	4	-1	-4	6	2

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Quadratic twists for elliptic curve 12584m1

-4	8	-3	-11
25168l1	100672x1	113256v1	12584a1

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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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