Hyperelliptic curves with reduced automorphism group A5

We study genus g hyperelliptic curves with reduced automorphism group A5 and give equations y2 = f(x) for such curves in both cases where f(x) is a decomposable polynomial in x2 or x5 . For any fixed genus the locus of such curves is a rational variety. We show that for every point in this locus there exists a rational model y2 = F(x) or y2 = xF(x) of the curve over its field of moduli where F(x) can be chosen to be decomposable in x2 or x5 . Such rational models appear in [1].

• Type: Journal
• Year: 2007
• Where: AAECC
• Authors: David Sevilla, Tanush Shaska
• Keywords: AAECC 2007, Algorithms, Decomposable Polynomial, Hyperelliptic Curves, Rational Models