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	2706q	Isogeny class
Conductor	2706	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	3550272 = 26 · 3 · 11 · 412	Discriminant
Eigenvalues	2- 3- -4  2 11+ -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-110,-444]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	147281603041/3550272	j-invariant
L	4.6434047091703	L(r)(E,1)/r!
Ω	1.4762800855852	Real period
R	1.0484470967512	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	21648v1 86592t1 8118j1 67650d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706q1

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
-	-	-4	2	+	-2	-6	0	-4	-10	8	6	+	-10	-6	-2	-2	-12	-12	14	-6	-6	0	-8	10

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Quadratic twists for elliptic curve 2706q1

-4	8	-3	5	-11	41
21648v1	86592t1	8118j1	67650d1	29766x1	110946ba1

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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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