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	2139f	Isogeny class
Conductor	2139	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-1790343 = -1 · 34 · 23 · 312	Discriminant
Eigenvalues	1 3- -2  2  0 -2 -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,28,29]	[a1,a2,a3,a4,a6]
Generators	[3:10:1]	Generators of the group modulo torsion
j	2554497863/1790343	j-invariant
L	4.0187434946594	L(r)(E,1)/r!
Ω	1.6746626937363	Real period
R	1.1998665491537	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	34224y1 6417m1 53475h1 104811c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2139f1

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	2	0	-2	-4	6	+	-6	-	-4	-2	-8	-12	-12	0	4	-10	-12	14	-8	4	12	14

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Quadratic twists for elliptic curve 2139f1

-4	-3	5	-7	-23	-31
34224y1	6417m1	53475h1	104811c1	49197r1	66309d1

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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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