M. Alaa

collaborators

2 papers

math.NT2016

High rank quadratic twists of pairs of elliptic curves

Mohammad Sadek, Mohamed Alaa

Given a pair of elliptic curves $E_{1}$ and $E_{2}$ over the rational field $Q$ whose $j$ -invariants are not simultaneously 0 or 1728, Kuwata and Wang proved the existence of i…

math.NT2016

On geometric progressions on hyperelliptic curves

Mohamed Alaa, Mohammad Sadek

Let $C$ be a hyperelliptic curve over $Q$ described by $y^{2} = a_{0} x^{n} + a_{1} x^{n - 1} + \dots + a_{n}$ , $a_{i} \in Q$ . The points $P_{i} = (x_{i}, y_{i}) \in C (Q)$ , $i=1,2,...,…