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Modular and Shimura curves embedded in
Oana Padurariu
We classify the modular curves that admit a smooth embedding in and obtain a partial classification for the Shimura curves . We…
Unexpected primes of good reduction in quotients of modular and Shimura curves
Oana Padurariu, Sun Woo Park, John Voight
We find all zero-dimensional spaces of newforms of weight and squarefree level with a fixed Atkin--Lehner sign pattern. As an application, we classify unexpected primes of…
Shimura curve Atkin--Lehner quotients of genus at most two
Oana Padurariu, Frederick Saia
We provide a complete enumeration of all quotients of genus and of the Shimura curves over by non-trivial subgroups of Atkin--Lehner involutions.…
Point counts, automorphisms, and gonalities of Shimura curves
Pietro Mercuri, Oana Padurariu, Frederick Saia +1
We implement an algorithm to compute the number of points over finite fields for the Shimura curves over and their Atkin--Lehner quotients. Our computations…
Counting 5-isogenies of elliptic curves over
Santiago Arango-Piñeros, Changho Han, Oana Padurariu +1
We show that the number of -isogenies of elliptic curves defined over with naive height bounded by is asymptotic to for some e…
Bielliptic Shimura curves with nontrivial level
Oana Padurariu, Frederick Saia
We work towards completely classifying all bielliptic Shimura curves with nontrivial level coprime to , extending a result of Rotger that provided such a classifi…
Shimura curves admitting a smooth plane model
Oana Padurariu
We prove that there are no Shimura curves of squarefree level and of genus at least two admitting a smooth plane model.
Rational points on rank 2 genus 2 bielliptic curves in the LMFDB
Francesca Bianchi, Oana Padurariu
Building on work of Balakrishnan, Dogra, and of the first author, we provide some improvements to the explicit quadratic Chabauty method to compute rational points on genus bie…
Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves
Oana Padurariu, Ciaran Schembri
Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves . In this paper we compute the -rational points on the Atkin-Lehner qu…
Cyclic isogenies of elliptic curves over fixed quadratic fields
Barinder S. Banwait, Filip Najman, Oana Padurariu
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cyclic isogenies of elliptic curves over . Although more than 40 years ha…
Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings
Nikola Adžaga, Shiva Chidambaram, Timo Keller +1
We complete the computation of all -rational points on all the maximal Atkin-Lehner quotients such that the quotient is hyperelliptic. To achieve this,…