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	3718o	Isogeny class
Conductor	3718	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	-6317018703424 = -1 · 26 · 112 · 138	Discriminant
Eigenvalues	2- -2  3  2 11+ 13+ -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4989,181297]	[a1,a2,a3,a4,a6]
j	-16835377/7744	j-invariant
L	2.8147225836202	L(r)(E,1)/r!
Ω	0.70368064590505	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	29744bd1 118976bk1 33462bk1 92950e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718o1

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	2	+	+	-3	2	0	-3	8	11	9	-4	-6	3	6	-7	14	12	-7	-10	6	6	-10

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Quadratic twists for elliptic curve 3718o1

-4	8	-3	5	-11	13
29744bd1	118976bk1	33462bk1	92950e1	40898t1	3718k1

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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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