Cremona's table of elliptic curves

2666 = 2 · 31 · 43

Field	Data	Notes
Atkin-Lehner	2- 31- 43+	Signs for the Atkin-Lehner involutions
Class	2666d	Isogeny class
Conductor	2666	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	682496 = 29 · 31 · 43	Discriminant
Eigenvalues	2-  0 -1 -2  5 -1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-208,1203]	[a1,a2,a3,a4,a6]
Generators	[9:-3:1]	Generators of the group modulo torsion
j	990728800209/682496	j-invariant
L	4.2747626863324	L(r)(E,1)/r!
Ω	2.8398571843158	Real period
R	0.16725264722393	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	21328h1 85312j1 23994j1 66650g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2666d1

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	-1	-2	5	-1	2	-4	-4	-2	-	0	3	+	-11	-9	-6	0	2	-14	13	6	4	-5	-1

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Quadratic twists for elliptic curve 2666d1

-4	8	-3	5	-31	-43
21328h1	85312j1	23994j1	66650g1	82646g1	114638f1

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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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