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	2706i	Isogeny class
Conductor	2706	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	5412 = 22 · 3 · 11 · 41	Discriminant
Eigenvalues	2+ 3- -4  0 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-28,-58]	[a1,a2,a3,a4,a6]
Generators	[6:-2:1]	Generators of the group modulo torsion
j	2305199161/5412	j-invariant
L	2.303036942245	L(r)(E,1)/r!
Ω	2.0847089325971	Real period
R	2.2094565876647	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	21648o1 86592d1 8118n1 67650bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706i1

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	0	-	-2	-2	4	6	0	-4	2	+	8	-12	-10	-4	-4	12	0	-6	4	4	-6	-18

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Quadratic twists for elliptic curve 2706i1

-4	8	-3	5	-11	41
21648o1	86592d1	8118n1	67650bv1	29766bw1	110946c1

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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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