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	1710s	Isogeny class
Conductor	1710	Conductor
∏ cp	224	Product of Tamagawa factors cp
deg	17920	Modular degree for the optimal curve
Δ	-85832326981877760 = -1 · 228 · 311 · 5 · 192	Discriminant
Eigenvalues	2- 3- 5-  4  0  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,33088,13895651]	[a1,a2,a3,a4,a6]
j	5495662324535111/117739817533440	j-invariant
L	3.5691849063025	L(r)(E,1)/r!
Ω	0.2549417790216	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13680bx1 54720bl1 570d1 8550h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710s1

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	2	2	+	0	-10	0	2	-2	-4	0	6	-8	6	12	0	-14	0	12	-10	2

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Quadratic twists for elliptic curve 1710s1

-4	8	-3	5	-7	-19
13680bx1	54720bl1	570d1	8550h1	83790ed1	32490z1

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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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