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	1710n	Isogeny class
Conductor	1710	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	17100721620 = 22 · 38 · 5 · 194	Discriminant
Eigenvalues	2- 3- 5+ -4  4 -6  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8708,314867]	[a1,a2,a3,a4,a6]
Generators	[57:7:1]	Generators of the group modulo torsion
j	100162392144121/23457780	j-invariant
L	3.6862290672039	L(r)(E,1)/r!
Ω	1.2008857915947	Real period
R	1.5347958536126	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	13680bf3 54720cp4 570e3 8550g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710n4

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
-	-	+	-4	4	-6	6	+	-4	-6	-8	2	-10	-8	-12	-2	4	-2	-12	16	-14	8	0	6	14

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Quadratic twists for elliptic curve 1710n4

-4	8	-3	5	-7	-19
13680bf3	54720cp4	570e3	8550g4	83790fs4	32490l4

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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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