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	1710r	Isogeny class
Conductor	1710	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	4038951600 = 24 · 312 · 52 · 19	Discriminant
Eigenvalues	2- 3- 5-  2  6  0 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-14567,-673041]	[a1,a2,a3,a4,a6]
j	468898230633769/5540400	j-invariant
L	3.4765593570941	L(r)(E,1)/r!
Ω	0.43456991963676	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13680bw2 54720bg2 570a2 8550f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710r2

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	6	0	-2	+	-4	8	-8	-4	4	-6	12	-6	4	2	-8	0	6	8	-4	4	12

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Quadratic twists for elliptic curve 1710r2

-4	8	-3	5	-7	-19
13680bw2	54720bg2	570a2	8550f2	83790et2	32490x2

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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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