## Diagonalizable quartic Thue equations with negative discriminant

### Volume 193 / 2020

Acta Arithmetica 193 (2020), 235-252
MSC: Primary 11D45.
DOI: 10.4064/aa180402-12-3
Published online: 7 February 2020

#### Abstract

The Thue–Siegel method is applied to derive an upper bound for the number of solutions to Thue’s equation $F(x,y) = 1$ where $F$ is a quartic diagonalizable form with negative discriminant. Computation is used to handle forms whose discriminant is small in absolute value. We then apply our results to bound the number of integral points on a certain family of elliptic curves.