Fast enumeration of s.sp. hyperelliptic curves of genus 4 with automorphism group V4
Magma codes, log files and a table of results
Magma codes, log files and a table of results
The codes below work over Magma V.2.25-3 (or later versions).
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.
Here is a code enumerates s.sp. hyperelliptic curves of genus 4 with automorphism group V4.
A code for finding a single s.sp. curve (with automorphism group containing V4) and its log file:
A code for finding a single s.sp. curve (with automorphism group containing V4) and its log file:
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.)
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.)