Everett W. Howe

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math.NT2026

Curves of genus two with maps of every degree to a fixed elliptic curve

Everett W. Howe

We show that up to isomorphism there are exactly twenty pairs $(C, E)$ , where $C$ is a genus- $2$ curve over $C$ , where $E$ is an elliptic curve over $C$ , and whe…

math.NT2024

Enumerating places of $P^{1}$ up to automorphisms of $P^{1}$ in quasilinear time

Everett W. Howe

We present an algorithm that, for every fixed degree $n \geq 3$ , will enumerate all degree- $n$ places of the projective line over a finite field $k$ up to the natural action of $\ope…

math.NT2024

Doubly isogenous curves of genus two with a rational action of $D_{6}$

Jeremy Booher, Everett W. Howe, Andrew V. Sutherland +1

Let $C$ and $C^{'}$ be curves over a finite field $K$ , provided with embeddings $ι$ and $ι^{'}$ into their Jacobian varieties. Let $D \to C$ and $D^{'} \to C^{'}$ be the pullbacks (via these emb…

math.NT2024

Enumerating hyperelliptic curves over finite fields in quasilinear time

Everett W. Howe

We present an algorithm that, for every fixed genus $g$ , will enumerate all hyperelliptic curves of genus $g$ over a finite field $k$ of odd characteristic in quasilinear time; tha…

Curves of genus two with maps of every degree to a fixed elliptic curve

Enumerating places of P1 up to automorphisms of P1 in quasilinear time

Doubly isogenous curves of genus two with a rational action of D6​

Enumerating hyperelliptic curves over finite fields in quasilinear time

Enumerating places of $P^{1}$ up to automorphisms of $P^{1}$ in quasilinear time

Doubly isogenous curves of genus two with a rational action of $D_{6}$