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	1734c	Isogeny class
Conductor	1734	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	34261143524226 = 2 · 320 · 173	Discriminant
Eigenvalues	2+ 3+  2  2  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-21094,-1153910]	[a1,a2,a3,a4,a6]
Generators	[885:25525:1]	Generators of the group modulo torsion
j	211293405175481/6973568802	j-invariant
L	2.1671407506986	L(r)(E,1)/r!
Ω	0.3969499066413	Real period
R	5.4594816989261	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	13872bj4 55488bm4 5202k4 43350da4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734c4

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
+	+	2	2	0	-6	+	0	-6	-6	-10	-2	0	-4	8	6	0	-10	8	-10	16	6	16	10	-12

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Quadratic twists for elliptic curve 1734c4

-4	8	-3	5	-7	17
13872bj4	55488bm4	5202k4	43350da4	84966bz4	1734f4

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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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