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arXiv · 2211.06019

Explicit bounds on the coefficients of modular polynomials for the elliptic $j$-invariant

Florian Breuer·Fabien Pazuki
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Abstract

We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials $Φ_N$ for any $N\geq1$. These polynomials vanish at pairs of $j$-invariants of elliptic curves linked by cyclic isogenies of degree $N$. The main term in the bound is asymptotically optimal as $N$ tends to infinity.

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Florian Breuer, Fabien Pazuki. 2023-10-05. Explicit bounds on the coefficients of modular polynomials for the elliptic $j$-invariant. https://arxiv.org/abs/2211.06019

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