Abstract
Let and be two elliptic curves over a number field. We prove that the reductions of and at a finite place are geometrically isogenous for infinitely many , and we draw consequences for the existence of supersingular primes. This result is an analogue for distributions of Frobenius traces of known results on the density of Noether–Lefschetz loci in Hodge theory. The proof relies on dynamical properties of the Hecke correspondences on the modular curve.
Citation
François Charles. "Exceptional isogenies between reductions of pairs of elliptic curves." Duke Math. J. 167 (11) 2039 - 2072, 15 August 2018. https://doi.org/10.1215/00127094-2018-0011
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