Cremona's table of elliptic curves

1587 = 3 · 23²

Field	Data	Notes
Atkin-Lehner	3- 23-	Signs for the Atkin-Lehner involutions
Class	1587d	Isogeny class
Conductor	1587	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	7728	Modular degree for the optimal curve
Δ	-171266124809547 = -1 · 37 · 238	Discriminant
Eigenvalues	-2 3-  0  1  4 -3 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-20278,-1284182]	[a1,a2,a3,a4,a6]
Generators	[176:793:1]	Generators of the group modulo torsion
j	-11776000/2187	j-invariant
L	1.8419249193617	L(r)(E,1)/r!
Ω	0.19804217596815	Real period
R	0.44288904632062	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	25392v1 101568a1 4761f1 39675m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1587d1

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
-2	-	0	1	4	-3	-8	-4	-	-4	-8	-1	8	1	-6	6	6	15	-13	-10	-14	-8	-6	2	2

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Quadratic twists for elliptic curve 1587d1

-4	8	-3	5	-7	-23
25392v1	101568a1	4761f1	39675m1	77763s1	1587e1

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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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