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	-29657628081619848 = -1 · 23 · 312 · 178	Discriminant
Eigenvalues	2+ 3+  0 -2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-62285,10194117]	[a1,a2,a3,a4,a6]
Generators	[-127:4073:1]	Generators of the group modulo torsion
j	-1107111813625/1228691592	j-invariant
L	1.8045805560692	L(r)(E,1)/r!
Ω	0.33786000618935	Real period
R	2.6706039824344	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	13872be2 55488bc2 5202h2 43350cy2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734b2

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 1734b2

-4	8	-3	5	-7	17
13872be2	55488bc2	5202h2	43350cy2	84966bs2	102c2

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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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