Fast enumeration of s.sp. hyperelliptic curves of genus 4 with automorphism group V4

Magma codes, log files and a table of results

The codes below work over Magma V.2.25-3 (or later versions).

Here is a code enumerates s.sp. hyperelliptic curves of genus 4 with automorphism group V4.

• Code (txt): ver0, ver1

• Log file (txt): file0 (+file01), file1

A code for finding a single s.sp. curve (with automorphism group containing V4) and its log file:

• Code (txt): ver0, ver1

• Log file (txt): file0 (+file01), file1

Note that the improved code ver1 is much more efficient than ver0, and with ver1, we can find a s.sp. hyperelliptic curve of genus 4 for much larger p (in our computational environment, we succeeded in finding such a curve for p up to 5000 within a day.)