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Maarten Derickx

Number theory seminar on March 18, 2011 at 3:30pm in Padelford C401.


Torsion points on elliptic curves over number fields of small degree.


Merel has shown that if we fix $d \geq 1$, then there are only finitely many primes $p$ occurring as the order of a torsion point on an elliptic curve $E/K$ where $K$ is a number field of degree $\leq d$. Oesterle has proven that the largest such $p$ is smaller then $(3^{d/2}+1)^2$. Both upper bounds use a criterion by Kammienny. In my talk I will show several variations on this criterion. I will also show how to bring down the bound for $d=5$ and $d=6$ using this criterion using a computer program based on William Steins work on $d=4$.


2013-05-11 18:34