Cremona's table of elliptic curves

1770 = 2 · 3 · 5 · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 59+	Signs for the Atkin-Lehner involutions
Class	1770g	Isogeny class
Conductor	1770	Conductor
∏ cp	208	Product of Tamagawa factors cp
deg	1664	Modular degree for the optimal curve
Δ	-79277875200 = -1 · 213 · 38 · 52 · 59	Discriminant
Eigenvalues	2- 3- 5+ -3 -3 -5  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-721,15401]	[a1,a2,a3,a4,a6]
Generators	[26:107:1]	Generators of the group modulo torsion
j	-41454067728529/79277875200	j-invariant
L	4.2144481369548	L(r)(E,1)/r!
Ω	0.96722218201891	Real period
R	0.02094841316285	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	14160o1 56640q1 5310g1 8850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1770g1

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
-	-	+	-3	-3	-5	1	-2	0	-6	-2	-5	1	1	-4	0	+	-2	4	-9	6	1	15	-16	0

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Quadratic twists for elliptic curve 1770g1

-4	8	-3	5	-7	-59
14160o1	56640q1	5310g1	8850b1	86730cf1	104430l1

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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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