Cremona's table of elliptic curves

2139 = 3 · 23 · 31

Field	Data	Notes
Atkin-Lehner	3+ 23+ 31+	Signs for the Atkin-Lehner involutions
Class	2139a	Isogeny class
Conductor	2139	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	49197 = 3 · 232 · 31	Discriminant
Eigenvalues	1 3+  0  0  0  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-495,-4452]	[a1,a2,a3,a4,a6]
Generators	[1046:11309:8]	Generators of the group modulo torsion
j	13455798261625/49197	j-invariant
L	3.21591282084	L(r)(E,1)/r!
Ω	1.0118920185399	Real period
R	6.3562371516287	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	34224bm2 6417i2 53475l2 104811r2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2139a2

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	+	0	0	0	6	-2	-4	+	6	+	-8	-6	10	4	-6	0	-8	-16	0	-10	-2	-4	-6	-6

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Quadratic twists for elliptic curve 2139a2

-4	-3	5	-7	-23	-31
34224bm2	6417i2	53475l2	104811r2	49197c2	66309l2

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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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