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	3718s	Isogeny class
Conductor	3718	Conductor
∏ cp	46	Product of Tamagawa factors cp
deg	71760	Modular degree for the optimal curve
Δ	-978526871039770624 = -1 · 223 · 11 · 139	Discriminant
Eigenvalues	2-  0  3 -1 11- 13-  8  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-645781,-205175187]	[a1,a2,a3,a4,a6]
j	-2808592297029/92274688	j-invariant
L	3.8660483870232	L(r)(E,1)/r!
Ω	0.084044530152679	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	29744x1 118976w1 33462bc1 92950u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718s1

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
-	0	3	-1	-	-	8	4	-5	3	8	-2	-9	-9	10	6	-1	-1	7	14	5	16	-6	-8	2

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Quadratic twists for elliptic curve 3718s1

-4	8	-3	5	-11	13
29744x1	118976w1	33462bc1	92950u1	40898w1	3718d1

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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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