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
deg	10368	Modular degree for the optimal curve
Δ	95409498488832 = 218 · 39 · 11 · 412	Discriminant
Eigenvalues	2- 3-  0 -2 11+ -6  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-11508,69264]	[a1,a2,a3,a4,a6]
Generators	[-60:768:1]	Generators of the group modulo torsion
j	168548786637666625/95409498488832	j-invariant
L	5.0917874442312	L(r)(E,1)/r!
Ω	0.51704121622854	Real period
R	0.12157942425577	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	21648s1 86592l1 8118g1 67650c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706o1

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 2706o1

-4	8	-3	5	-11	41
21648s1	86592l1	8118g1	67650c1	29766u1	110946w1

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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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