Cremona's table of elliptic curves

1659 = 3 · 7 · 79

Field	Data	Notes
Atkin-Lehner	3- 7- 79+	Signs for the Atkin-Lehner involutions
Class	1659d	Isogeny class
Conductor	1659	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1244483919 = 38 · 74 · 79	Discriminant
Eigenvalues	-1 3- -2 7- -4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-504,3969]	[a1,a2,a3,a4,a6]
Generators	[-21:84:1]	Generators of the group modulo torsion
j	14160193117057/1244483919	j-invariant
L	1.9945623665783	L(r)(E,1)/r!
Ω	1.4949288196377	Real period
R	0.66710947717956	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	26544l4 106176g4 4977b3 41475a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1659d3

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	-	-4	-2	6	0	8	-2	-4	-2	-2	-12	0	-2	4	2	-4	0	-14	+	-16	2	-6

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Quadratic twists for elliptic curve 1659d3

-4	8	-3	5	-7
26544l4	106176g4	4977b3	41475a4	11613a3

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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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