# Heights and isogenies of Drinfeld modules

## TL;DR

This paper establishes explicit bounds on the heights of isogenous Drinfeld modules, proves finiteness in their isogeny classes, and provides bounds on modular polynomial coefficients in rank 2, advancing understanding in function field arithmetic.

## Contribution

It introduces explicit bounds on heights and coefficients of Drinfeld modules, and proves finiteness results in isogeny classes, enhancing the theoretical framework of Drinfeld modules.

## Key findings

- Explicit bounds on height differences of isogenous Drinfeld modules
- Finiteness results in isogeny classes of Drinfeld modules
- Explicit upper bounds on modular polynomial coefficients in rank 2

## Abstract

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.