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	1710o	Isogeny class
Conductor	1710	Conductor
∏ cp	216	Product of Tamagawa factors cp
Δ	1316983574361600 = 29 · 37 · 52 · 196	Discriminant
Eigenvalues	2- 3- 5+  2  0  2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-67298,6505697]	[a1,a2,a3,a4,a6]
j	46237740924063961/1806561830400	j-invariant
L	2.8714999056885	L(r)(E,1)/r!
Ω	0.47858331761474	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	13680bc4 54720bs4 570f4 8550l4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710o4

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

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Quadratic twists for elliptic curve 1710o4

-4	8	-3	5	-7	-19
13680bc4	54720bs4	570f4	8550l4	83790ez4	32490j4

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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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