Cremona's table of elliptic curves

5187 = 3 · 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 13- 19+	Signs for the Atkin-Lehner involutions
Class	5187g	Isogeny class
Conductor	5187	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-323995098609 = -1 · 38 · 7 · 135 · 19	Discriminant
Eigenvalues	-1 3- -1 7+  3 13-  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2671,-59998]	[a1,a2,a3,a4,a6]
Generators	[179:-2371:1]	Generators of the group modulo torsion
j	-2107441550633329/323995098609	j-invariant
L	2.7321833465046	L(r)(E,1)/r!
Ω	0.32925723111578	Real period
R	0.20745051955623	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	82992cc1 15561g1 129675j1 36309e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187g1

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	-	-1	+	3	-	0	+	-6	0	5	-9	0	8	-8	4	-7	8	8	-2	-6	-13	10	8	-2

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Quadratic twists for elliptic curve 5187g1

-4	-3	5	-7	13	-19
82992cc1	15561g1	129675j1	36309e1	67431s1	98553b1

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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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