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	2706n	Isogeny class
Conductor	2706	Conductor
∏ cp	140	Product of Tamagawa factors cp
Δ	1225076438754432 = 27 · 32 · 1110 · 41	Discriminant
Eigenvalues	2- 3+ -4  2 11- -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-38055,-2324259]	[a1,a2,a3,a4,a6]
Generators	[-121:786:1]	Generators of the group modulo torsion
j	6094802039817492721/1225076438754432	j-invariant
L	3.4883875899349	L(r)(E,1)/r!
Ω	0.346630603206	Real period
R	0.28753438367371	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	21648bd2 86592bf2 8118d2 67650bi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706n2

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	2	-8	8	2	0	-10	+	2	-6	-2	-6	-4	-4	-10	-14	2	-16	8	10

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Quadratic twists for elliptic curve 2706n2

-4	8	-3	5	-11	41
21648bd2	86592bf2	8118d2	67650bi2	29766n2	110946bh2

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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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