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
Δ	13428016272 = 24 · 33 · 11 · 414	Discriminant
Eigenvalues	2- 3- -2  0 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-25379,-1558287]	[a1,a2,a3,a4,a6]
Generators	[-92:49:1]	Generators of the group modulo torsion
j	1807791328511035057/13428016272	j-invariant
L	4.877434100752	L(r)(E,1)/r!
Ω	0.37825182549951	Real period
R	1.0745561933312	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	21648q4 86592g4 8118a3 67650l4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706r3

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 2706r3

-4	8	-3	5	-11	41
21648q4	86592g4	8118a3	67650l4	29766s4	110946t4

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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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