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	1710h	Isogeny class
Conductor	1710	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	16621200 = 24 · 37 · 52 · 19	Discriminant
Eigenvalues	2+ 3- 5-  0 -4  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-279,-1715]	[a1,a2,a3,a4,a6]
Generators	[-9:7:1]	Generators of the group modulo torsion
j	3301293169/22800	j-invariant
L	2.2663038697833	L(r)(E,1)/r!
Ω	1.1684397374661	Real period
R	0.96979921048301	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	13680br1 54720bc1 570g1 8550x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710h1

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

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Quadratic twists for elliptic curve 1710h1

-4	8	-3	5	-7	-19
13680br1	54720bc1	570g1	8550x1	83790bo1	32490bv1

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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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