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

Proceedings of the American Mathematical Society, Series B Pub Date : 2024-07-01 DOI:10.1090/bproc/179

Florian Breuer, Fabien Pazuki

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引用次数: 0

Abstract

We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials Φ N \Phi _N for any N ≥ 1 N\geq 1 . These polynomials vanish at pairs of j j -invariants of elliptic curves linked by cyclic isogenies of degree N N . The main term in the bound is asymptotically optimal as N N tends to infinity.