This volume contains the proceedings of the LMFDB, Computation, and Number Theory (LuCaNT) 2025 conference, held at the Institute for Computational and Experimental Research in Mathematics (ICERM), from July 7-11, 2025, in Providence, Rhode Island. This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database, http://lmfdb.org), an online resource for mathematical objects arising in the Langlands program and the connections between them.
Jordi Guardia-Rubies, John W. Jones, Kevin Keating, Sebastian Pauli,
David P. Roberts, and David Roe, Families of $p$-adic fields; Fabian
Gundlach, Sampling cubic rings; Noam D. Elkies, A Shimura-Belyi map of degree
33, and number fields with Galois group 33T55 = $\Sigma
\mathrm{L}_2(\mathbf{F}_{32})$; David W. Farmer, Sally Koutsoliotas, Stefan
Lemurell, and David P. Roberts, Fine structure in some landscapes of
L-functions; David Lowry-Duda, Computing a database of rigorous Maass forms;
Taha Hedayat, Sarah Arpin, and Renate Scheidler, The spine of a supersingular
$\ell$-isogeny graph; Edgar Costa, Andreas-Stephan Elsenhans, Jorg Jahnel,
and John Voight, Explicit modularity of K3 surfaces with complex
multiplication of large degree; Sven Cats, John Michael Clark, Charlotte
Dombrowsky, Mar Curco Iranzo, Krystal Maughan, and Eli Orvis, Experimental
investigations on Lehmer's conjecture for elliptic curves; Lewis Combes, John
Jones, Jennifer Paulhus, David Roe, Manami Roy, and Sam Schiavone, Creating a
dynamic database of finite groups; Steven Clontz, Database-driven
mathematical inquiry and the $\Pi$-base model for small semantic databases;
Stevan Gajovic, Jeroen Hanselman, and Angelos Koutsianas, Local-global
principle for 11-isogenies of elliptic curves is true over quadratic fields;
Kate Finnerty, Quadratic Chabauty experiments on genus 2 biellliptic modular
curves in the LMFDB; Pitchayut Saengrungkongka and Noah Walsh, Gluing genus 1
and genus 2 curves along $\ell$-torsion; Yongyuan Huang, Kiran S. Kedlaya,
and Jun Bo Lau, A census of genus 6 curves over $\mathbb{F}_2$; Adam Logan,
The Kodaira dimension of Hilbert modular threefolds; Shiva Chidambaram,
Computing the mod-3 Galois image of a principally polarized abelian surface
over the rationals; Jennifer Paulhus and Andrew V. Sutherland, Completely
decomposable modular Jacobians; Edgar Costa, Taylor Dupuy, Stefano Marseglia,
David Roe, and Christelle Vincent, Labeling abelian varieties over finite
fields; Craig Costello and Gaurish Korpal, On pairs of primes with small
order reciprocity; Asimina S. Hamakiotes and Jun Bo Lau, Genus formulas for
families of modular curves; Maria Corte-Real Santos, Jonathan Komada Eriksen,
Antonin Leroux, Michael Meyer, and Lorenz Panny, Evaluation of modular
polynomial from supersingular elliptic curves; Marco Streng, Explicit
supersingular cyclic curves; Raymond van Bommel, Edgar Costa, Bjorn Poonen,
and Padmavathi Srinivasan, Curve equations from expansions of 1-forms at a
nonrational point
John W. Jones, Arizona State University, Tempe, Arizona.
Jennifer Paulhus, Mount Holyoke College, South Hadley, Massachusetts.
Andrew V. Sutherland, Massachusetts Institute of Technology, Cambridge, Massachusetts.
John Voight, University of Sydney, Australia
