On the elliptic curves induced by the diophantine M-tuples

Diophantine equations form the basis of mathematical studies on integers, especially with daily life applications. Elliptic curves, on the other hand, have attracted the attention of scien-tists in recent years, especially because they have a wide application area and are used in the proof of Fermat's Last Theorem. In this study, these two concepts were brought together in the same pot. The rank and torsion groups of elliptic curves reduced by Diophantine m -tuples have been investigated, and this compilation study is specialized for various values of m. The thesis work ends with the study of a current article.