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	2706p	Isogeny class
Conductor	2706	Conductor
∏ cp	198	Product of Tamagawa factors cp
deg	4752	Modular degree for the optimal curve
Δ	-449959048704 = -1 · 29 · 311 · 112 · 41	Discriminant
Eigenvalues	2- 3- -1 -4 11+  1 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1641,41049]	[a1,a2,a3,a4,a6]
Generators	[150:-1857:1]	Generators of the group modulo torsion
j	-488726621230609/449959048704	j-invariant
L	4.7955179298663	L(r)(E,1)/r!
Ω	0.85705260527822	Real period
R	0.028259394318876	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	21648t1 86592n1 8118h1 67650f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706p1

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
-	-	-1	-4	+	1	-3	-3	8	2	-7	-6	+	-4	-12	-8	-11	-6	9	5	-9	12	-9	-5	10

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Quadratic twists for elliptic curve 2706p1

-4	8	-3	5	-11	41
21648t1	86592n1	8118h1	67650f1	29766v1	110946y1

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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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