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	3	Product of Tamagawa factors cp
Δ	-62424 = -1 · 23 · 33 · 172	Discriminant
Eigenvalues	2- 3+  3  4 -3  2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-130124,-18121147]	[a1,a2,a3,a4,a6]
j	-843137281012581793/216	j-invariant
L	3.393469534165	L(r)(E,1)/r!
Ω	0.12568405682093	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872bl2 55488bs2 5202c2 43350bj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734j2

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 1734j2

-4	8	-3	5	-7	17
13872bl2	55488bs2	5202c2	43350bj2	84966dx2	1734l2

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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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