In this thesis we will introduce some basic notions on the arithmetic theory of elliptic curves and show how this theory is connected to the congruent number problem, a classical problem in arithmetic. The main result is the close connection between congruent numbers and a the rank of the Mordell-Weil group of a specific family of rational elliptic curves with complex multiplication.
In this thesis we will introduce some basic notions on the arithmetic theory of elliptic curves and show how this theory is connected to the congruent number problem, a classical problem in arithmetic. The main result is the close connection between congruent numbers and a the rank of the Mordell-Weil group of a specific family of rational elliptic curves with complex multiplication.
Elliptic curves and the congruent number problem
BARBAN, FRANCESCO
2022/2023
Abstract
In this thesis we will introduce some basic notions on the arithmetic theory of elliptic curves and show how this theory is connected to the congruent number problem, a classical problem in arithmetic. The main result is the close connection between congruent numbers and a the rank of the Mordell-Weil group of a specific family of rational elliptic curves with complex multiplication.| File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/52082