Cremona's table of elliptic curves

2639 = 7 · 13 · 29

Field	Data	Notes
Atkin-Lehner	7- 13- 29-	Signs for the Atkin-Lehner involutions
Class	2639a	Isogeny class
Conductor	2639	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-34307 = -1 · 7 · 132 · 29	Discriminant
Eigenvalues	2  3  0 7-  0 13-  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-55,157]	[a1,a2,a3,a4,a6]
j	-18399744000/34307	j-invariant
L	7.3617849233816	L(r)(E,1)/r!
Ω	3.6808924616908	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42224k1 23751f1 65975e1 18473b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2639a1

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
2	3	0	-	0	-	2	3	1	-	-4	12	-9	4	-9	1	4	-2	-15	-15	9	10	4	-3	5

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Quadratic twists for elliptic curve 2639a1

-4	-3	5	-7	13	29
42224k1	23751f1	65975e1	18473b1	34307g1	76531c1

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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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