Cremona's table of elliptic curves

2581 = 29 · 89

Field	Data	Notes
Atkin-Lehner	29+ 89+	Signs for the Atkin-Lehner involutions
Class	2581a	Isogeny class
Conductor	2581	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	624	Modular degree for the optimal curve
Δ	-193185269 = -1 · 293 · 892	Discriminant
Eigenvalues	-1 -1 -1  2 -5 -1  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,99,592]	[a1,a2,a3,a4,a6]
Generators	[8:40:1]	Generators of the group modulo torsion
j	107239576751/193185269	j-invariant
L	1.5647084487074	L(r)(E,1)/r!
Ω	1.229939532498	Real period
R	0.63609161562987	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	41296c1 23229m1 64525a1 126469a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2581a1

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	-1	-1	2	-5	-1	6	4	-2	+	3	-2	12	5	-3	3	-14	-6	0	14	10	15	-6	+	12

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Quadratic twists for elliptic curve 2581a1

-4	-3	5	-7	29
41296c1	23229m1	64525a1	126469a1	74849b1

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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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