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	5187k	Isogeny class
Conductor	5187	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-254163 = -1 · 3 · 73 · 13 · 19	Discriminant
Eigenvalues	2 3- -2 7- -1 13+ -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-14,-37]	[a1,a2,a3,a4,a6]
Generators	[42:59:8]	Generators of the group modulo torsion
j	-325660672/254163	j-invariant
L	7.7208886977541	L(r)(E,1)/r!
Ω	1.1869382095386	Real period
R	2.1682927933701	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	82992bk1 15561m1 129675g1 36309q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187k1

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	-	-1	+	-2	+	-4	5	2	-3	3	-13	-6	1	-12	0	-1	12	-11	4	8	-6	-14

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Quadratic twists for elliptic curve 5187k1

-4	-3	5	-7	13	-19
82992bk1	15561m1	129675g1	36309q1	67431m1	98553r1

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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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