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	2139c	Isogeny class
Conductor	2139	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1296	Modular degree for the optimal curve
Δ	519777 = 36 · 23 · 31	Discriminant
Eigenvalues	-1 3- -2  0 -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10829,432840]	[a1,a2,a3,a4,a6]
j	140440148435570257/519777	j-invariant
L	0.73524009921284	L(r)(E,1)/r!
Ω	1.9606402645676	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	34224bb1 6417h1 53475c1 104811e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2139c1

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	0	-4	-2	2	-4	+	6	+	6	10	4	-8	6	4	-2	-4	0	-6	-8	4	10	18

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Quadratic twists for elliptic curve 2139c1

-4	-3	5	-7	-23	-31
34224bb1	6417h1	53475c1	104811e1	49197k1	66309e1

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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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