Cremona's table of elliptic curves

3718 = 2 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	3718q	Isogeny class
Conductor	3718	Conductor
∏ cp	180	Product of Tamagawa factors cp
Δ	-2736726872129536 = -1 · 215 · 113 · 137	Discriminant
Eigenvalues	2- -2 -3  1 11- 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,9883,-2487551]	[a1,a2,a3,a4,a6]
Generators	[1522:58727:1]	Generators of the group modulo torsion
j	22117051943/566984704	j-invariant
L	3.20698321643	L(r)(E,1)/r!
Ω	0.21971836716466	Real period
R	0.081088229693874	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	29744q2 118976l2 33462x2 92950n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718q2

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	-3	1	-	+	6	-8	-3	9	-2	10	-9	-1	0	6	3	-7	7	-12	1	-4	0	-12	4

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Quadratic twists for elliptic curve 3718q2

-4	8	-3	5	-11	13
29744q2	118976l2	33462x2	92950n2	40898u2	286a2

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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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