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	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	4977 = 32 · 7 · 79	Discriminant
Eigenvalues	-1 3- -2 7- -4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-104,-417]	[a1,a2,a3,a4,a6]
Generators	[19:58:1]	Generators of the group modulo torsion
j	124475734657/4977	j-invariant
L	1.9945623665783	L(r)(E,1)/r!
Ω	1.4949288196377	Real period
R	2.6684379087183	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26544l1 106176g1 4977b1 41475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1659d1

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 1659d1

-4	8	-3	5	-7
26544l1	106176g1	4977b1	41475a1	11613a1

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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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