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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 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…