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	2739g	Isogeny class
Conductor	2739	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-2739 = -1 · 3 · 11 · 83	Discriminant
Eigenvalues	0 3+  3 -2 11- -2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	32768/2739	j-invariant
L	2.653472105773	L(r)(E,1)/r!
Ω	3.473462653011	Real period
R	0.76392705805336	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	43824z1 8217e1 68475g1 30129c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2739g1

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	+	3	-2	-	-2	-3	-1	8	-5	-8	-3	10	-1	8	-3	10	-14	-12	1	1	1	-	10	-16

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Quadratic twists for elliptic curve 2739g1

-4	-3	5	-11
43824z1	8217e1	68475g1	30129c1

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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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