# Sixteenth Algorithmic Number Theory Symposium (ANTS XVI)

Massachusetts Institute of Technology

July 15–19, 2024

## Papers presented at ANTS XVI

- Barinder S. Banwait, Maarten Derickx,
(code)*Torsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville* - Daniel Bernstein, Jolijn Cottaar, Tanja Lange,
(code)*Searching for differential addition chains* - Francesca Bianchi, Enis Kaya, Jan Steffen Müller,
(code)*Algorithms for p-adic Heights on hyperelliptic curves of arbitrary reduction* - Raymond van Bommel, Jordan Docking, Reynald Lercier, Elisa Lorenzo García,
(code)*Reduction of plane quartics and Dixmier-Ohno invariants* - Colby Austin Brown,
(code)*An almost linear time algorithm testing whether the Markoff graph modulo p is connected* - Xavier Caruso, Quentin Gazda,
(code)*Computation of classical and v-adic L-series of t-motives* - Maria Corte-Real Santos, Craig Costello, Benjamin Smith,
(code)*Efficient (3,3)-isogenies on fast Kummer surfaces* - Edgar Costa, Kiran S. Kedlaya, David Roe,
(code)*Hypergeometric L-functions in average polynomial time, II* - Noam D. Elkies,
*Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bound* - Steven D. Galbraith,
*Climbing and descending tall volcanos* - Everett W. Howe,
(code)*Enumerating hyperelliptic curves over finite fields in quasilinear time* - Aashraya Jha,
(code)*Finding integral points on elliptic curves over imaginary quadratic fields* - Seungki Kim, Phong Q. Nguyen,
(data)*On counterexamples to the Mertens conjecture* - Sabrina Kunzweiler, Damien Robert,
(code)*Computing modular polynomials by deformation* - Sumin Leem, Michael J. Jacobson, Renate Scheidler,
(code)*Solving norm equations in global function fields* - Martin Lüdtke,
(code)*Refined Chabauty-Kim computations for the thrice-punctured line over ℤ[1/6]* - Céline Maistret, Andrew V. Sutherland,
(code)*Computing Euler factors of genus 2 curves at odd primes of almost good reduction* - Stefano Marseglia,
(code)*Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields* - Erik Mulder,
(code)*Fast square-free decomposition of integers using class groups* - Oana Padurariu, Frederick Saia,
(code)*Bielliptic Shimura curves \(\boldsymbol{X_0^D(N)}\) with nontrivial level* - Aaron Pollack,
(code)*Computation of Fourier coefficients of automorphic forms of type G*_{2} - Andrew Shallue, Jonathan Webster,
(code)*Advances in tabulating Carmichael numbers* - Joseph H. Silverman,
*A heuristic subexponential algorithm to find paths in Markoff graphs over finite fields* - Jonathan Sorenson, Jonathan Webster,
(code)*An algorithm and computation to verify Legendre's conjecture up to 7·10*^{13} - José Felipe Voloch,
*Factoring polynomials over function fields* - David Zywina,
(code)*Open image computations for elliptic curves over number fields*

We are grateful to the Mathematics Research Data Initiative (MaRDI) for reviewing the code and data linked to above.