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	8	Product of Tamagawa factors cp
Δ	-169504391772536832 = -1 · 215 · 32 · 112 · 416	Discriminant
Eigenvalues	2+ 3-  0 -4 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,127379,9293864]	[a1,a2,a3,a4,a6]
Generators	[6038:182107:8]	Generators of the group modulo torsion
j	228571521134288888375/169504391772536832	j-invariant
L	2.6810599749715	L(r)(E,1)/r!
Ω	0.20546669870608	Real period
R	6.524317545995	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	21648m4 86592a4 8118k4 67650by4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706g4

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 2706g4

-4	8	-3	5	-11	41
21648m4	86592a4	8118k4	67650by4	29766bq4	110946a4

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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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