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	2706l	Isogeny class
Conductor	2706	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	17973252 = 22 · 35 · 11 · 412	Discriminant
Eigenvalues	2- 3+  0 -2 11-  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-83,173]	[a1,a2,a3,a4,a6]
Generators	[-1:16:1]	Generators of the group modulo torsion
j	63282696625/17973252	j-invariant
L	3.9553351846692	L(r)(E,1)/r!
Ω	2.0318836200173	Real period
R	1.9466347116059	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	21648y1 86592z1 8118b1 67650bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706l1

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

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Quadratic twists for elliptic curve 2706l1

-4	8	-3	5	-11	41
21648y1	86592z1	8118b1	67650bg1	29766g1	110946bd1

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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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