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	5187a	Isogeny class
Conductor	5187	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	4560	Modular degree for the optimal curve
Δ	-1333313163 = -1 · 33 · 7 · 135 · 19	Discriminant
Eigenvalues	-2 3+ -2 7+ -3 13-  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-624,6464]	[a1,a2,a3,a4,a6]
Generators	[26:84:1]	Generators of the group modulo torsion
j	-26913692127232/1333313163	j-invariant
L	1.2311455639561	L(r)(E,1)/r!
Ω	1.5078900142119	Real period
R	0.16329381484757	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	82992cq1 15561h1 129675bj1 36309v1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187a1

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	+	-2	+	-3	-	6	-	-4	3	-6	1	-9	11	-6	-9	4	4	11	8	15	0	-12	-14	6

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Quadratic twists for elliptic curve 5187a1

-4	-3	5	-7	13	-19
82992cq1	15561h1	129675bj1	36309v1	67431e1	98553w1

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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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