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Conic fibrations over elliptic curves

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Simon Myerson
University of Warwick
Mit, 22/03/2023 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Contact: Pieter Moree (moree @

A theorem of Serre states that almost all plane conics over Q have no rational point. We prove an analogue of this for a family of conics parametrised by certain elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve. Another way to think about this result is: we show that 0% of points on elliptic curves have a denominator which is a sum of two squares.

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