M. Sadek

collaborators

3 papers

math.NT2016

On dependence of rational points on elliptic curves

Mohammad Sadek

Let $E$ be an elliptic curve defined over $Q$ . Let $Γ$ be a subgroup of $E (Q)$ and $P \in E (Q)$ . In [1], it was proved that if $E$ has no nontrivial rational…

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,...,…

math.NT2011

Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve

Mohammad Sadek

Let E be an elliptic curve defined over a number field K. Let h be an element of order 4 in the Shafarevich-Tate group of E. We prove that h is visible in infinitely many abelian s…