Cremona's table of elliptic curves

1710 = 2 · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	1710b	Isogeny class
Conductor	1710	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-49904640 = -1 · 210 · 33 · 5 · 192	Discriminant
Eigenvalues	2+ 3+ 5- -2 -2 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,81,173]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1]	Generators of the group modulo torsion
j	2161700757/1848320	j-invariant
L	2.1762892416983	L(r)(E,1)/r!
Ω	1.3011095265311	Real period
R	0.83632053924792	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	13680x1 54720b1 1710l1 8550u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710b1

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	-2	-4	6	-	8	-6	-8	-8	-12	0	0	10	-6	-6	12	12	-10	-8	-8	-8	-14

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Quadratic twists for elliptic curve 1710b1

-4	8	-3	5	-7	-19
13680x1	54720b1	1710l1	8550u1	83790d1	32490bg1

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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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