Superspecial trigonal curves of genus $5$

Abstract

This paper provides an algorithm enumerating superspecial trigonal curves of genus $5$ over finite fields. Executing the algorithm over a computer algebra system Magma, we enumerate them over finite fields ${\mathbb{F}}_{p^a}$ for any natural number $a$ if $p\le 7$ and for odd $a$ if $p\le 13$.

References in corpus (4)

• Superspecial curves of genus $4$ in small characteristic
• Enumerating superspecial curves of genus $4$ over prime fields
• Automorphism groups of superspecial curves of genus $4$ over ${\mathbb{F}}_{11}$
• Superspecial trigonal curves of genus $5$

Cited by in corpus (1)

• Superspecial trigonal curves of genus $5$