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	12	Product of Tamagawa factors cp
Δ	-107191841427 = -1 · 36 · 116 · 83	Discriminant
Eigenvalues	-1 3+  4  0 11-  0  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-306,-16014]	[a1,a2,a3,a4,a6]
j	-3169397364769/107191841427	j-invariant
L	1.3824838683139	L(r)(E,1)/r!
Ω	0.46082795610462	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	43824bd2 8217f2 68475h2 30129f2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2739f2

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 2739f2

-4	-3	5	-11
43824bd2	8217f2	68475h2	30129f2

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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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