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	3718m	Isogeny class
Conductor	3718	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	6552	Modular degree for the optimal curve
Δ	-71784303448 = -1 · 23 · 11 · 138	Discriminant
Eigenvalues	2-  2 -4 -2 11+ 13+  8 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-595,13801]	[a1,a2,a3,a4,a6]
j	-28561/88	j-invariant
L	2.8839420645787	L(r)(E,1)/r!
Ω	0.96131402152623	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29744bg1 118976bn1 33462bm1 92950g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718m1

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	-4	-2	+	+	8	-1	1	1	0	10	10	11	-1	-10	14	-2	8	-3	-4	8	9	-1	-1

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Quadratic twists for elliptic curve 3718m1

-4	8	-3	5	-11	13
29744bg1	118976bn1	33462bm1	92950g1	40898q1	3718i1

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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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