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
deg	13440	Modular degree for the optimal curve
Δ	13306760282112 = 214 · 3 · 115 · 412	Discriminant
Eigenvalues	2- 3+ -4  2 11- -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-11815,457181]	[a1,a2,a3,a4,a6]
Generators	[-89:946:1]	Generators of the group modulo torsion
j	182400988413112561/13306760282112	j-invariant
L	3.4883875899349	L(r)(E,1)/r!
Ω	0.693261206412	Real period
R	0.14376719183686	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	21648bd1 86592bf1 8118d1 67650bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706n1

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 2706n1

-4	8	-3	5	-11	41
21648bd1	86592bf1	8118d1	67650bi1	29766n1	110946bh1

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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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