Cremona's table of elliptic curves

3887 = 13² · 23

Field	Data	Notes
Atkin-Lehner	13+ 23+	Signs for the Atkin-Lehner involutions
Class	3887a	Isogeny class
Conductor	3887	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4680	Modular degree for the optimal curve
Δ	-431521551409 = -1 · 138 · 232	Discriminant
Eigenvalues	1 -2  3 -2  0 13+ -3  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,503,-31263]	[a1,a2,a3,a4,a6]
Generators	[885:3431:27]	Generators of the group modulo torsion
j	17303/529	j-invariant
L	3.3976305400344	L(r)(E,1)/r!
Ω	0.45436195623733	Real period
R	1.2463009917508	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	62192q1 34983n1 97175l1 3887b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3887a1

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	-2	3	-2	0	+	-3	8	+	5	4	-5	-1	0	-12	-5	-4	-1	-10	6	-9	12	-6	10	-6

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Quadratic twists for elliptic curve 3887a1

-4	-3	5	13	-23
62192q1	34983n1	97175l1	3887b1	89401c1

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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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