3 citations · 11 across the 13 of their papers we have counts for
13 papers
Thin sets in weighted projective stacks
Stephanie Chan, Daniel Loughran, Nick Rome
We prove an upper bound for the number of rational points of bounded height in a weighted projective stack which lie in a given thin subset. As a consequence, we show that …
Selmer groups of families of elliptic curves with an -isogeny
Stephanie Chan, Matteo Verzobio
For certain families of elliptic curves admitting a rational isogeny of prime degree , we establish a central limit theorem for the Tamagawa ratio and derive bounds on its av…
Number fields generated by points in linear systems on curves
Irmak Balçik, Stephanie Chan, Yuan Liu +1
We develop techniques for determining the fibers of a morphism of curves over a nonarchimedean local field . These results have applications to studying closed poin…
Solubility of a resultant equation and applications
Tim Browning, Stephanie Chan
The large sieve is used to estimate the density of integral quadratic polynomials , such that there exists an odd degree integral polynomial which has resultant with …
Almost all elliptic curves with prescribed torsion have Szpiro ratio close to the expected value
Stephanie Chan
We demonstrate that almost all elliptic curves over with prescribed torsion subgroup, when ordered by naive height, have Szpiro ratio arbitrarily close to the expected…
The -isogeny Selmer groups of the elliptic curves
Stephanie Chan
Consider the family of elliptic curves , where varies over positive cubefree integers. There is a rational -isogeny from to $\hat{E}_n:y^2=x^3-27n…
The average number of integral points on the congruent number curves
Stephanie Chan
We show that the total number of non-torsion integral points on the elliptic curves , where ranges over positive squarefree integers less than ,…
A Density of Ramified Primes
Stephanie Chan, Christine McMeekin, Djordjo Milovic
Let be a cyclic totally real number field of odd degree over with odd class number, such that every totally positive unit is the square of a unit, and such that $2…
Integral points on the congruent number curve
Stephanie Chan
We study integral points on the quadratic twists of the congruent number curve. We give upper bounds on the number of integral points in each coset of…
On the negative Pell equation
Stephanie Chan, Peter Koymans, Djordjo Milovic +1
Using a recent breakthrough of Smith, we improve the results of Fouvry and Klüners on the solubility of the negative Pell equation. Let denote the set of fundamental…
Kuroda's formula and arithmetic statistics
Stephanie Chan, Djordjo Milovic
Kuroda's formula relates the class number of a multi-quadratic number field to the class numbers of its quadratic subfields . A key component in this formula is the unit g…
Ranks, -Selmer groups, and Tamagawa numbers of elliptic curves with -torsion
Stephanie Chan, Jeroen Hanselman, Wanlin Li
In 2016, Balakrishnan-Ho-Kaplan-Spicer-Stein-Weigandt produced a database of elliptic curves over ordered by height in which they computed the rank, the size of the $2…
Rational Right Triangles of a Given Area
Stephanie Chan
Starting from any given rational-sided, right triangle, for example the -triangle with area , we use Euclidean geometry to show that there are infinitely many other rat…