Cremona's table of elliptic curves

1734 = 2 · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 17+	Signs for the Atkin-Lehner involutions
Class	1734f	Isogeny class
Conductor	1734	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	28009982077085412 = 22 · 310 · 179	Discriminant
Eigenvalues	2+ 3- -2 -2  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-6047187,-5724215366]	[a1,a2,a3,a4,a6]
j	206226044828441/236196	j-invariant
L	0.96274493715361	L(r)(E,1)/r!
Ω	0.096274493715361	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13872w3 55488i3 5202j3 43350ca3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734f3

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

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Quadratic twists for elliptic curve 1734f3

-4	8	-3	5	-7	17
13872w3	55488i3	5202j3	43350ca3	84966t3	1734c3

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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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