Theoretical Foundations of Applied Discrete Mathematics

Calculation of $3$-torsion ideal for some class of hyperelliptic curves

E. S. Malygina

Immanuel Kant Baltic Federal University, Kaliningrad

Abstract: In the paper, we consider hyperelliptic curves of genus two defined by the Dickson polynomials. For such curves, we calculate the $3$-torsion ideal, namely we obtain the four generators of this ideal by using the Mumford–Cantor representation for the $3$-torsion divisor and by using of $\theta$- and $\wp$-functions.

Keywords: hyperelliptic curve, Dickson polynomial, $l$-torsion ideal, $l$-torsion divisor, modular equation.

UDC: 512.772.7

DOI: 10.17223/2226308X/12/3

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