Cremona's table of elliptic curves

1339 = 13 · 103

Field	Data	Notes
Atkin-Lehner	13- 103+	Signs for the Atkin-Lehner involutions
Class	1339b	Isogeny class
Conductor	1339	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-17407 = -1 · 132 · 103	Discriminant
Eigenvalues	1  0  0 -4  6 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2,7]	[a1,a2,a3,a4,a6]
j	-1157625/17407	j-invariant
L	1.6456872246133	L(r)(E,1)/r!
Ω	3.2913744492267	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21424r1 85696a1 12051e1 33475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1339b1

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

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Quadratic twists for elliptic curve 1339b1

-4	8	-3	5	-7	13
21424r1	85696a1	12051e1	33475a1	65611b1	17407b1

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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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