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	1710c	Isogeny class
Conductor	1710	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	-209551579545600000 = -1 · 220 · 311 · 55 · 192	Discriminant
Eigenvalues	2+ 3- 5+ -2 -2  4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,84015,19909341]	[a1,a2,a3,a4,a6]
j	89962967236397039/287450726400000	j-invariant
L	0.89405924430326	L(r)(E,1)/r!
Ω	0.22351481107581	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	13680be1 54720ch1 570l1 8550y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710c1

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

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Quadratic twists for elliptic curve 1710c1

-4	8	-3	5	-7	-19
13680be1	54720ch1	570l1	8550y1	83790ch1	32490bn1

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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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