Elliptic curves

Thursday, August 24, 2017 - 9:00am - 9:45am
Kiran Kedlaya (University of California, San Diego)
We give a survey of some of the ways that number theorists use Sage. Among the basic objects we will encounter are elliptic curves, modular forms, and L-functions (including zeta functions).
Monday, January 3, 2011 - 3:40pm - 4:40pm
Karl Rubin (University of California)
In joint work with Barry Mazur, we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions for an elliptic curve to have twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) with a given 2-Selmer rank. As a consequence, under appropriate hypotheses there are many twists with Mordell-Weil rank zero, and (assuming the Shafarevich-Tate conjecture) many others with Mordell-Weil rank one.
Monday, January 3, 2011 - 2:00pm - 3:00pm
Carl Pomerance (Dartmouth College)
In the past three decades there have been some exciting
applications of elliptic curves over finite fields
to integer factoring, primality testing, and
cryptography. These applications in turn have raised some interesting
problems often of an unconventional flavor. For example, how
often is the order of an elliptic curve group prime, or how
often does it have all small prime factors? In this talk we will
visit problems such as these, as well as other analytic-type
problems relating to ranks of elliptic curves over function
Tuesday, January 4, 2011 - 3:30pm - 4:30pm
Manjul Bhargava (Princeton University)
No Abstract
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