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	2706o	Isogeny class
Conductor	2706	Conductor
∏ cp	324	Product of Tamagawa factors cp
Δ	984060439515648 = 29 · 318 · 112 · 41	Discriminant
Eigenvalues	2- 3-  0 -2 11+ -6  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-116468,-15233904]	[a1,a2,a3,a4,a6]
Generators	[-188:256:1]	Generators of the group modulo torsion
j	174720473725693794625/984060439515648	j-invariant
L	5.0917874442312	L(r)(E,1)/r!
Ω	0.25852060811427	Real period
R	0.24315884851155	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	21648s2 86592l2 8118g2 67650c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706o2

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	+	-6	2	-8	-8	-2	0	-2	+	6	6	10	6	0	12	2	-6	-2	0	-8	-14

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Quadratic twists for elliptic curve 2706o2

-4	8	-3	5	-11	41
21648s2	86592l2	8118g2	67650c2	29766u2	110946w2

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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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