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	2666b	Isogeny class
Conductor	2666	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	10640	Modular degree for the optimal curve
Δ	645426573737984 = 219 · 315 · 43	Discriminant
Eigenvalues	2+  0  1  2 -5 -3  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-24134,773172]	[a1,a2,a3,a4,a6]
Generators	[143:409:1]	Generators of the group modulo torsion
j	1554611083084760121/645426573737984	j-invariant
L	2.5399446308111	L(r)(E,1)/r!
Ω	0.46359725392161	Real period
R	1.095754821378	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	21328e1 85312g1 23994x1 66650n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2666b1

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	-3	6	4	0	2	-	-8	3	-	9	-11	-14	-8	-10	2	9	-6	-12	-1	-17

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Quadratic twists for elliptic curve 2666b1

-4	8	-3	5	-31	-43
21328e1	85312g1	23994x1	66650n1	82646a1	114638i1

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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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