Cremona's table of elliptic curves

2739 = 3 · 11 · 83

Field	Data	Notes
Atkin-Lehner	3+ 11- 83+	Signs for the Atkin-Lehner involutions
Class	2739d	Isogeny class
Conductor	2739	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	189501075753 = 3 · 113 · 834	Discriminant
Eigenvalues	1 3+  2 -4 11-  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2379,38472]	[a1,a2,a3,a4,a6]
j	1490020510656313/189501075753	j-invariant
L	1.4590194419168	L(r)(E,1)/r!
Ω	0.97267962794454	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43824bb1 8217g1 68475j1 30129h1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2739d1

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
1	+	2	-4	-	2	-2	-4	0	10	0	6	-2	4	-4	-14	12	14	-4	12	6	0	+	6	18

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Quadratic twists for elliptic curve 2739d1

-4	-3	5	-11
43824bb1	8217g1	68475j1	30129h1

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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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