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	2706g	Isogeny class
Conductor	2706	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	-69470644988448 = -1 · 25 · 36 · 116 · 412	Discriminant
Eigenvalues	2+ 3-  0 -4 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-30526,2089040]	[a1,a2,a3,a4,a6]
Generators	[-110:2084:1]	Generators of the group modulo torsion
j	-3145668549383265625/69470644988448	j-invariant
L	2.6810599749715	L(r)(E,1)/r!
Ω	0.61640009611824	Real period
R	2.1747725153317	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	21648m2 86592a2 8118k2 67650by2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706g2

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

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Quadratic twists for elliptic curve 2706g2

-4	8	-3	5	-11	41
21648m2	86592a2	8118k2	67650by2	29766bq2	110946a2

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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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