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	1734i	Isogeny class
Conductor	1734	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3030800878069216722 = -1 · 2 · 32 · 1714	Discriminant
Eigenvalues	2- 3+  2  0  4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-475122,-151542927]	[a1,a2,a3,a4,a6]
j	-491411892194497/125563633938	j-invariant
L	2.8709968885608	L(r)(E,1)/r!
Ω	0.089718652767525	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13872bi6 55488bl5 5202b6 43350ba5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734i6

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

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Quadratic twists for elliptic curve 1734i6

-4	8	-3	5	-7	17
13872bi6	55488bl5	5202b6	43350ba5	84966dv5	102b6

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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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