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	1710g	Isogeny class
Conductor	1710	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-29550046959360 = -1 · 28 · 311 · 5 · 194	Discriminant
Eigenvalues	2+ 3- 5+  4  0 -6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-17100,-895280]	[a1,a2,a3,a4,a6]
Generators	[323:5054:1]	Generators of the group modulo torsion
j	-758575480593601/40535043840	j-invariant
L	2.2323440489626	L(r)(E,1)/r!
Ω	0.20809985080627	Real period
R	2.6818184159113	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	13680bd1 54720bx1 570i1 8550bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710g1

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

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Quadratic twists for elliptic curve 1710g1

-4	8	-3	5	-7	-19
13680bd1	54720bx1	570i1	8550bh1	83790bs1	32490bo1

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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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