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
Δ	137917 = 13 · 1032	Discriminant
Eigenvalues	1  0  0 -4  6 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-67,228]	[a1,a2,a3,a4,a6]
j	33542015625/137917	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	21424r2 85696a2 12051e2 33475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1339b2

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 1339b2

-4	8	-3	5	-7	13
21424r2	85696a2	12051e2	33475a2	65611b2	17407b2

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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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