Computation of superspecial Howe curves of genus 3

In the below codes, algorithms (Methods 1, 2 and 3) proposed in Section 5 of arXiv: 2209.02926 are implemented on Magma.

Each of the following codes computes a single example of superspecial Howe curves of genus 3.

• Code for hyperelliptic case: ver. 1

• Code for non-hyperelliptic case: ver. 1

Each of the below codes enumerates superspecial Howe curves of genus 3.

• Hyperelliptic case:

  • Method 1 (ver. 1) with isomorphism classification over finite fields F_{p^2}.

  • Method 1 (ver. 1) with isomorphism classification over an algebraic closure.

  • Method 2 (ver. 1) with isomorphism classification over finite fields F_{p^2}.

  • Method 2 (ver. 1) with isomorphism classification over an algebraic closure.

• Non-hyperelliptic case: Method 3 (ver. 1).