Eli Orvis

activity

20202025

collaborators

5 papers

math.NT2025

Experimental investigations on Lehmer's conjecture for elliptic curves

Sven Cats, John Michael Clark, Charlotte Dombrowsky +3

In this short note, we give a method for computing a non-torsion point of smallest canonical height on a given elliptic curve $E / Q$ over all number fields of a fixed degre…

math.NT2025

Zeta functions of abstract isogeny graphs and modular curves

Jun Bo Lau, Travis Morrison, Eli Orvis +2

We introduce a ``non-orientable'' variation of Serre's definition of a graph, which we call an abstract isogeny graph. These objects capture the combinatorics of the graphs $G(p,\e…

math.NT2025

Hypergeometric decomposition of Delsarte K3 pencils

Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro +4

We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeomet…

math.NT2024

Distribution of cycles in supersingular $ℓ$ -isogeny graphs

Eli Orvis

Recent work by Arpin, Chen, Lauter, Scheidler, Stange, and Tran counted the number of cycles of length $r$ in supersingular $ℓ$ -isogeny graphs. In this paper, we extend this wor…

math.NT2020

Newly reducible polynomial iterates

Peter Illig, Rafe Jones, Eli Orvis +2

Given a field $K$ and $n > 1$ , we say that a polynomial $f \in K [x]$ has newly reducible $n$ th iterate over $K$ if $f^{n - 1}$ is irreducible over $K$ , but $f^{n}$ is not (here $f^{i}$ d…

Experimental investigations on Lehmer's conjecture for elliptic curves

Zeta functions of abstract isogeny graphs and modular curves

Hypergeometric decomposition of Delsarte K3 pencils

Distribution of cycles in supersingular ℓ-isogeny graphs

Newly reducible polynomial iterates

Distribution of cycles in supersingular $ℓ$ -isogeny graphs