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	3718k	Isogeny class
Conductor	3718	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1308736 = -1 · 26 · 112 · 132	Discriminant
Eigenvalues	2+ -2 -3 -2 11- 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-30,80]	[a1,a2,a3,a4,a6]
Generators	[-3:13:1] [2:4:1]	Generators of the group modulo torsion
j	-16835377/7744	j-invariant
L	2.2073501673741	L(r)(E,1)/r!
Ω	2.5371566503623	Real period
R	0.21750235318153	Regulator
r	2	Rank of the group of rational points
S	0.99999999999919	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29744r1 118976m1 33462cm1 92950ch1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718k1

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 3718k1

-4	8	-3	5	-11	13
29744r1	118976m1	33462cm1	92950ch1	40898bw1	3718o1

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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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