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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Extremal primes for non-CM elliptic curves 
 
Thu, Aug 02, 2018,   04:00 PM to 05:00 PM at Madhava Hall

Dr. Neha Prabhu
Queen\'s University

 For an elliptic curve $E$ over $\\mathbb{Q}$, the distribution of the number of points on $E$ mod $p$ has been well-studied over the last few decades. A relatively recent study is that of extremal primes for a given curve $E$. These are the primes $p$ of good reduction for which the number of points on $E$ mod $p$ is either maximal or minimal. If $E$ is a curve with CM, an asymptotic for the number of extremal primes was determined by James and Pollack. The talk will discuss the non-CM case and focus on obtaining upper bounds. This is joint work with C. David, A. Gafni, A. Malik and C. Turnage-Butterbaugh. 

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