Coefficients of modular polynomials

Abstract: For a positive integer $N$, denote by $\Phi_N(X,Y)$ the elliptic modular polynomial of level $N$ -- it vanishes at pairs of $j$-invariants of elliptic curves linked by a cyclic isogeny of degree $N$ and plays an important role in various cryptosystems. The coefficients of $\Phi_N$ are notoriously large. In this talk, I present joint work with Fabien Pazuki and Desir'ee Gij\'on G\'omez proving explicit upper and lower bounds on the size of these coefficients.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html