Cremona's table of elliptic curves

2706 = 2 · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 41-	Signs for the Atkin-Lehner involutions
Class	2706r	Isogeny class
Conductor	2706	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	798031872 = 216 · 33 · 11 · 41	Discriminant
Eigenvalues	2- 3- -2  0 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-339,1953]	[a1,a2,a3,a4,a6]
Generators	[-18:57:1]	Generators of the group modulo torsion
j	4309261738417/798031872	j-invariant
L	4.877434100752	L(r)(E,1)/r!
Ω	1.513007301998	Real period
R	0.2686390483328	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21648q1 86592g1 8118a1 67650l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706r1

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	0	-	-6	-6	-4	4	-2	-8	6	-	0	0	-6	-8	14	-4	-8	10	0	-4	-2	2

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Quadratic twists for elliptic curve 2706r1

-4	8	-3	5	-11	41
21648q1	86592g1	8118a1	67650l1	29766s1	110946t1

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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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