Cremona's table of elliptic curves

1587 = 3 · 23²

Field	Data	Notes
Atkin-Lehner	3- 23-	Signs for the Atkin-Lehner involutions
Class	1587c	Isogeny class
Conductor	1587	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-30643429023 = -1 · 32 · 237	Discriminant
Eigenvalues	1 3-  0  2 -4 -6 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-276,8581]	[a1,a2,a3,a4,a6]
Generators	[343:6176:1]	Generators of the group modulo torsion
j	-15625/207	j-invariant
L	3.88562272784	L(r)(E,1)/r!
Ω	0.99543576208274	Real period
R	1.951719475956	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392x1 101568c1 4761c1 39675j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1587c1

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	2	-4	-6	-4	-2	-	2	4	-2	2	-10	0	12	-12	6	10	8	-14	-10	-12	16	10

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Quadratic twists for elliptic curve 1587c1

-4	8	-3	5	-7	-23
25392x1	101568c1	4761c1	39675j1	77763f1	69a1

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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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