Eleni Agathocleous

collaborators

3 papers

math.NT2025

Elliptic Curves with positive rank and no integral points

Eleni Agathocleous

We consider all \emph{odd} fundamental discriminants $D \equiv 2 mod 3$ and their mirror discriminants $D^{'} = - 3 D$ , and we study the family of elliptic curves $E_{D'}: y^{2} = x^{…

math.NT2024

On the Selmer group and rank of a family of elliptic curves and curves of genus one violating the Hasse principle

Eleni Agathocleous

We study an infinite family of $j$ -invariant zero elliptic curves $E_{D} : y^{2} = x^{3} + 16 D$ and their $I^»$ -isogenous curves $E_{D^{'}} : y^{2} = x^{3} - 27 \cdot 16 D$ , where $D$ and $D^{'} = - 3 D$ …

math.NT2024

Elliptic curves over Hasse pairs

Eleni Agathocleous, Antoine Joux, Daniele Taufer

We call a pair of distinct prime powers $(q_{1}, q_{2}) = (p_{1}^{a_{1}}, p_{2}^{a_{2}})$ a Hasse pair if $∣ q_{1} - q_{2} ∣ \leq 1$ . For such pairs, we study the relation between the set…