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	12734496 = 25 · 34 · 173	Discriminant
Eigenvalues	2+ 3+  2  2  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2904,59040]	[a1,a2,a3,a4,a6]
Generators	[33:6:1]	Generators of the group modulo torsion
j	551569744601/2592	j-invariant
L	2.1671407506986	L(r)(E,1)/r!
Ω	1.9847495332065	Real period
R	1.0918963397852	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	13872bj2 55488bm2 5202k2 43350da2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734c2

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 1734c2

-4	8	-3	5	-7	17
13872bj2	55488bm2	5202k2	43350da2	84966bz2	1734f2

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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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