This article is cited in 2 papers

Theoretical Foundations of Applied Discrete Mathematics

Characteristic polynomials of the curve $y^2=x^7+ax^4+bx$ over finite fields

S. A. Novoselov, Y. F. Boltnev

Immanuel Kant Baltic Federal University, Kaliningrad

Abstract: In this work, we list all possible characteristic polynomials of the Frobenius endomorphism for genus $3$ hyperelliptic curves of type $y^2 = x^7 + a x^4 + b x$ over finite field $\mathbb{F}_q$ of characteristic $p>3$.

Keywords: hyperelliptic curves, characteristic polynomials, point-counting, genus $3$.

UDC: 512.772.7

Language: English

DOI: 10.17223/2226308X/12/12

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