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	1734k	Isogeny class
Conductor	1734	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8568	Modular degree for the optimal curve
Δ	-24191926805388 = -1 · 22 · 3 · 1710	Discriminant
Eigenvalues	2- 3+ -4 -3  4 -5 17+  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1740,237561]	[a1,a2,a3,a4,a6]
j	-289/12	j-invariant
L	1.1193534075443	L(r)(E,1)/r!
Ω	0.55967670377217	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872bo1 55488bt1 5202d1 43350bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734k1

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	-3	4	-5	+	1	-6	4	7	-1	8	3	-6	12	-6	7	9	0	14	8	-2	0	-1

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Quadratic twists for elliptic curve 1734k1

-4	8	-3	5	-7	17
13872bo1	55488bt1	5202d1	43350bg1	84966ea1	1734m1

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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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