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	-2.4162509422393E+19	Discriminant
Eigenvalues	2+ 3+  0 -2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,522940,-186183984]	[a1,a2,a3,a4,a6]
Generators	[14590:654223:8]	Generators of the group modulo torsion
j	655215969476375/1001033261568	j-invariant
L	1.8045805560692	L(r)(E,1)/r!
Ω	0.11262000206312	Real period
R	8.0118119473032	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	13872be4 55488bc4 5202h4 43350cy4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734b4

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 1734b4

-4	8	-3	5	-7	17
13872be4	55488bc4	5202h4	43350cy4	84966bs4	102c4

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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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