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math.NT2020
Non-monogenic Division Fields of Elliptic Curves
Hanson Smith
For various positive integers , we show the existence of infinite families of elliptic curves over with -division fields, , that are not monoge…
math.NT2020
A Divisor Formula and a Bound on the -gonality of the Modular Curve
Mark van Hoeij, Hanson Smith
We give a formula for divisors of modular units on and use it to prove that the -gonality of the modular curve is bounded above by $\left[\frac{11N^2}…