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	5187c	Isogeny class
Conductor	5187	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	15561 = 32 · 7 · 13 · 19	Discriminant
Eigenvalues	1 3+  2 7- -4 13- -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-324,2115]	[a1,a2,a3,a4,a6]
j	3779648905033/15561	j-invariant
L	1.7283005935547	L(r)(E,1)/r!
Ω	3.4566011871094	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82992ci1 15561o1 129675v1 36309t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187c1

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	-	-4	-	-6	-	-8	6	0	10	10	4	8	6	4	-10	-4	8	-10	4	-4	10	2

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Quadratic twists for elliptic curve 5187c1

-4	-3	5	-7	13	-19
82992ci1	15561o1	129675v1	36309t1	67431b1	98553z1

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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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