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	3718h	Isogeny class
Conductor	3718	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	349440	Modular degree for the optimal curve
Δ	-17081218574058496 = -1 · 210 · 112 · 1310	Discriminant
Eigenvalues	2+  2 -3  2 11- 13+  1 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-76672599,-258441399211]	[a1,a2,a3,a4,a6]
j	-361585288790756017/123904	j-invariant
L	1.6326364415349	L(r)(E,1)/r!
Ω	0.025509944398983	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29744t1 118976p1 33462cl1 92950ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718h1

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	-	+	1	-6	8	1	0	-3	11	4	-6	11	14	5	6	-4	11	-6	-2	-6	-6

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Quadratic twists for elliptic curve 3718h1

-4	8	-3	5	-11	13
29744t1	118976p1	33462cl1	92950ck1	40898bs1	3718l1

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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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