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	2739f	Isogeny class
Conductor	2739	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	247569993 = 33 · 113 · 832	Discriminant
Eigenvalues	-1 3+  4  0 11-  0  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-721,-7714]	[a1,a2,a3,a4,a6]
j	41454067728529/247569993	j-invariant
L	1.3824838683139	L(r)(E,1)/r!
Ω	0.92165591220924	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	43824bd1 8217f1 68475h1 30129f1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2739f1

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	+	4	0	-	0	2	2	-4	2	8	10	10	-2	-6	0	-4	2	-8	-10	-12	2	+	12	10

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Quadratic twists for elliptic curve 2739f1

-4	-3	5	-11
43824bd1	8217f1	68475h1	30129f1

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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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