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	3718b	Isogeny class
Conductor	3718	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-1380467374 = -1 · 2 · 11 · 137	Discriminant
Eigenvalues	2+  2 -1  3 11+ 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3,-1789]	[a1,a2,a3,a4,a6]
Generators	[83:719:1]	Generators of the group modulo torsion
j	-1/286	j-invariant
L	3.6354846870421	L(r)(E,1)/r!
Ω	0.69543160204092	Real period
R	1.3069166961829	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	29744be1 118976bl1 33462cu1 92950bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718b1

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	-1	3	+	+	-6	0	1	-3	-10	-2	-7	-1	4	6	5	-11	1	-16	7	4	-4	-12	16

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Quadratic twists for elliptic curve 3718b1

-4	8	-3	5	-11	13
29744be1	118976bl1	33462cu1	92950bv1	40898bp1	286f1

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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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