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Friday, April 3, 2015

1:10 PM - 2:00 PM (ET)

ESC 638

Event Type

Lecture

Contact

Christopher Rasmussen,x2315

Department

Academic

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=48380

Abstract: Given an elliptic curve $E/\mathbb{Q}$, let $E[2^k]$ denote the set of points on $E$that have order dividing $2^k$. The coordinates of these points are algebraic numbersand using them, one can build a Galois representation $\rho : G_{\mathbb{Q}} \to \GL_{2}(\mathbb{Z}_{2})$.We give a classification of all possible images of this Galois representation. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.