Cremona's table of elliptic curves

1587 = 3 · 23²

Field	Data	Notes
Atkin-Lehner	3+ 23-	Signs for the Atkin-Lehner involutions
Class	1587b	Isogeny class
Conductor	1587	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8832	Modular degree for the optimal curve
Δ	-145893365578503 = -1 · 34 · 239	Discriminant
Eigenvalues	1 3+ -4 -4  0 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-36247,-2734160]	[a1,a2,a3,a4,a6]
j	-2924207/81	j-invariant
L	0.17271916180085	L(r)(E,1)/r!
Ω	0.17271916180085	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392bj1 101568bt1 4761d1 39675bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1587b1

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	+	-4	-4	0	-2	-4	-4	-	2	-8	8	-6	-4	0	4	-4	-8	-12	8	6	4	0	-12	-8

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Quadratic twists for elliptic curve 1587b1

-4	8	-3	5	-7	-23
25392bj1	101568bt1	4761d1	39675bf1	77763bc1	1587a1

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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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