Cremona's table of elliptic curves

3887 = 13² · 23

Field	Data	Notes
Atkin-Lehner	13+ 23+	Signs for the Atkin-Lehner involutions
Class	3887b	Isogeny class
Conductor	3887	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-89401 = -1 · 132 · 232	Discriminant
Eigenvalues	-1 -2 -3  2  0 13+ -3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3,-14]	[a1,a2,a3,a4,a6]
Generators	[5:9:1]	Generators of the group modulo torsion
j	17303/529	j-invariant
L	1.1266956961547	L(r)(E,1)/r!
Ω	1.6382253308338	Real period
R	0.34387689988326	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	62192r1 34983j1 97175i1 3887a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3887b1

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 3887b1

-4	-3	5	13	-23
62192r1	34983j1	97175i1	3887a1	89401d1

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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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