A genus two curve related to the class number one problem
نویسندگان
چکیده
منابع مشابه
On Siegel’s Modular Curve of Level 5 and the Class Number One Problem
Another derivation of an explicit parametrisation of Siegel’s modular curve of level 5 is obtained with applications to the class number one problem.
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It was first pointed out by Weil [26] that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2, 3, 4 were already known to the nineteenth centuary invariant theorists. We have succeeded in extending these methods to curves of degree n = 5, where although the invariants are too large to write down as explicit poly...
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Article history: Received 15 January 2015 Received in revised form 5 November 2015 Accepted 5 November 2015 Available online 4 January 2016 Communicated by David Goss MSC: primary 11R04 secondary 20H10
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Our aim in this paper is to prove that a smooth geometrically irreducible curve C of genus 4 over the finite field F8 may have at most 25 F8-points. Our strategy is as follows: if C has more than 18 F8-points, then C may not be hyperelliptic, and so the canonical divisor of C yields an embedding of C into P3F8 . The image of C under this embedding is a degree 6 curve which is precisely the inte...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.12.006