Cremona's table of elliptic curves

1660 = 2² · 5 · 83

Field	Data	Notes
Atkin-Lehner	2- 5+ 83-	Signs for the Atkin-Lehner involutions
Class	1660b	Isogeny class
Conductor	1660	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-33200 = -1 · 24 · 52 · 83	Discriminant
Eigenvalues	2- -1 5+ -3  5  2  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,46]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	-67108864/2075	j-invariant
L	2.2311636382324	L(r)(E,1)/r!
Ω	3.6726251849671	Real period
R	0.10125198942004	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6640c1 26560f1 14940b1 8300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1660b1

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	+	-3	5	2	3	6	-8	9	-9	-9	-10	-6	-6	-2	-1	-7	8	-12	-10	-4	-	10	16

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Quadratic twists for elliptic curve 1660b1

-4	8	-3	5	-7
6640c1	26560f1	14940b1	8300a1	81340h1

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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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