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	3718p	Isogeny class
Conductor	3718	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-60740564456 = -1 · 23 · 112 · 137	Discriminant
Eigenvalues	2- -1  1 -1 11- 13+ -1  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5665,162183]	[a1,a2,a3,a4,a6]
Generators	[161:1778:1]	Generators of the group modulo torsion
j	-4165509529/12584	j-invariant
L	4.4830196867127	L(r)(E,1)/r!
Ω	1.1131669519164	Real period
R	0.16780276006648	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	29744l1 118976d1 33462t1 92950k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718p1

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
-	-1	1	-1	-	+	-1	4	-8	-8	0	-7	8	11	1	2	-14	-8	-8	-9	4	2	0	4	-8

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Quadratic twists for elliptic curve 3718p1

-4	8	-3	5	-11	13
29744l1	118976d1	33462t1	92950k1	40898j1	286c1

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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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