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	4	Product of Tamagawa factors cp
Δ	234932955843 = 3 · 238	Discriminant
Eigenvalues	1 3-  0  2 -4 -6 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8211,284719]	[a1,a2,a3,a4,a6]
Generators	[22228:390365:64]	Generators of the group modulo torsion
j	413493625/1587	j-invariant
L	3.88562272784	L(r)(E,1)/r!
Ω	0.99543576208274	Real period
R	3.903438951912	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	25392x2 101568c2 4761c2 39675j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1587c2

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 1587c2

-4	8	-3	5	-7	-23
25392x2	101568c2	4761c2	39675j2	77763f2	69a2

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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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