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	2706g	Isogeny class
Conductor	2706	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	2442110888312832 = 230 · 3 · 11 · 413	Discriminant
Eigenvalues	2+ 3-  0 -4 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-36461,1232936]	[a1,a2,a3,a4,a6]
Generators	[14828840:139018899:64000]	Generators of the group modulo torsion
j	5360339745382407625/2442110888312832	j-invariant
L	2.6810599749715	L(r)(E,1)/r!
Ω	0.41093339741216	Real period
R	13.04863509199	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	21648m3 86592a3 8118k3 67650by3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706g3

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	-4	-	2	6	-4	-6	0	-4	2	+	8	0	-6	-12	8	-4	-12	2	8	-12	-6	-10

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Quadratic twists for elliptic curve 2706g3

-4	8	-3	5	-11	41
21648m3	86592a3	8118k3	67650by3	29766bq3	110946a3

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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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