Cremona's table of elliptic curves

1339 = 13 · 103

Field	Data	Notes
Atkin-Lehner	13+ 103+	Signs for the Atkin-Lehner involutions
Class	1339a	Isogeny class
Conductor	1339	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	280	Modular degree for the optimal curve
Δ	38243179 = 135 · 103	Discriminant
Eigenvalues	1 -1  1  4 -4 13+  3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-137,-602]	[a1,a2,a3,a4,a6]
Generators	[-6:10:1]	Generators of the group modulo torsion
j	287626699801/38243179	j-invariant
L	3.0228205315088	L(r)(E,1)/r!
Ω	1.406394723059	Real period
R	2.1493400692901	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21424i1 85696t1 12051b1 33475c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1339a1

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	-1	1	4	-4	+	3	-5	0	-3	0	-5	0	-12	6	-12	-5	-5	-4	-6	5	6	-1	-9	10

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Quadratic twists for elliptic curve 1339a1

-4	8	-3	5	-7	13
21424i1	85696t1	12051b1	33475c1	65611f1	17407c1

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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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