Hyperelliptic Curves

Features:

• Standard quadratic models, simplified models
• Invariants: degree, genus, discriminant
• Determination of points at infinity
• Heights of points on hyperelliptic curves
• Enumeration of all $\mbox{\bf Q}$-rational points up to a given height bound (Elkies-Stahlke-Stoll method)
• Reduction of a hyperelliptic curve from rational field to finite field
• Reduction types and conductors of a genus 2 curve at odd primes
• Zeta functions of hyperelliptic curves over finite fields
• Maps between hyperelliptic curves
• Jacobians of hyperelliptic curves