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	192	Product of Tamagawa factors cp
Δ	37959508224 = 28 · 36 · 112 · 412	Discriminant
Eigenvalues	2- 3- -2  0 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1619,-23391]	[a1,a2,a3,a4,a6]
Generators	[-26:49:1]	Generators of the group modulo torsion
j	469332926706097/37959508224	j-invariant
L	4.877434100752	L(r)(E,1)/r!
Ω	0.75650365099902	Real period
R	0.5372780966656	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21648q2 86592g2 8118a2 67650l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706r2

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 2706r2

-4	8	-3	5	-11	41
21648q2	86592g2	8118a2	67650l2	29766s2	110946t2

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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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