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	48	Product of Tamagawa factors cp
Δ	270168129729 = 312 · 232 · 312	Discriminant
Eigenvalues	-1 3- -2  0 -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10834,432419]	[a1,a2,a3,a4,a6]
j	140634771298875937/270168129729	j-invariant
L	0.73524009921284	L(r)(E,1)/r!
Ω	0.98032013228379	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	34224bb2 6417h2 53475c2 104811e2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2139c2

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 2139c2

-4	-3	5	-7	-23	-31
34224bb2	6417h2	53475c2	104811e2	49197k2	66309e2

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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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