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	1710q	Isogeny class
Conductor	1710	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-692550 = -1 · 2 · 36 · 52 · 19	Discriminant
Eigenvalues	2- 3- 5- -1  0 -3  7 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,13,-39]	[a1,a2,a3,a4,a6]
j	357911/950	j-invariant
L	2.9484226345433	L(r)(E,1)/r!
Ω	1.4742113172716	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13680bs1 54720bd1 190b1 8550d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710q1

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
-	-	-	-1	0	-3	7	+	5	5	10	2	-2	6	0	-9	7	-4	7	0	-9	-10	2	10	-18

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Quadratic twists for elliptic curve 1710q1

-4	8	-3	5	-7	-19
13680bs1	54720bd1	190b1	8550d1	83790ee1	32490u1

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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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