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	5187j	Isogeny class
Conductor	5187	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	64598830569 = 32 · 76 · 132 · 192	Discriminant
Eigenvalues	-1 3- -2 7- -4 13+ -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2204,37719]	[a1,a2,a3,a4,a6]
Generators	[-5:223:1]	Generators of the group modulo torsion
j	1184052061112257/64598830569	j-invariant
L	2.4685126904365	L(r)(E,1)/r!
Ω	1.0876006498481	Real period
R	0.75656222124707	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	82992bn2 15561k2 129675e2 36309o2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187j2

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	+	-2	+	8	2	8	-6	6	-4	12	-14	12	6	-16	0	-2	-8	-16	6	-2

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Quadratic twists for elliptic curve 5187j2

-4	-3	5	-7	13	-19
82992bn2	15561k2	129675e2	36309o2	67431l2	98553q2

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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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