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	1734j	Isogeny class
Conductor	1734	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	2268	Modular degree for the optimal curve
Δ	-2912454144 = -1 · 29 · 39 · 172	Discriminant
Eigenvalues	2- 3+  3  4 -3  2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1604,-25531]	[a1,a2,a3,a4,a6]
j	-1579268174113/10077696	j-invariant
L	3.393469534165	L(r)(E,1)/r!
Ω	0.37705217046278	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	13872bl1 55488bs1 5202c1 43350bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734j1

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
-	+	3	4	-3	2	+	8	-6	-3	7	-8	-6	-4	-6	-9	15	-14	2	0	7	1	12	0	13

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Quadratic twists for elliptic curve 1734j1

-4	8	-3	5	-7	17
13872bl1	55488bs1	5202c1	43350bj1	84966dx1	1734l1

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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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