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	1734b	Isogeny class
Conductor	1734	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	279783902667866112 = 218 · 32 · 179	Discriminant
Eigenvalues	2+ 3+  0 -2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-216900,-29485872]	[a1,a2,a3,a4,a6]
Generators	[1896:78924:1]	Generators of the group modulo torsion
j	46753267515625/11591221248	j-invariant
L	1.8045805560692	L(r)(E,1)/r!
Ω	0.22524000412623	Real period
R	4.0059059736516	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13872be3 55488bc3 5202h3 43350cy3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734b3

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
+	+	0	-2	0	2	+	-4	6	0	10	-8	-6	-4	12	6	-12	-8	-4	-6	-2	10	12	-18	-14

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Quadratic twists for elliptic curve 1734b3

-4	8	-3	5	-7	17
13872be3	55488bc3	5202h3	43350cy3	84966bs3	102c3

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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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