Folklore conjecture on ranks with prescribed torsion
Let be a torsion group, and let denote the family of elliptic curves over with torsion subgroup prescribed by . Folklore conjecture on ranks with prescribed torsion. The proportion of elliptic curves with rank in and the proportion of elliptic curves with rank in are both . The conjecture predicts the minimalist rank distribution within every prescribed-torsion family; the source says that evenly distributed root numbers and the authors' one-level density results provide small evidence toward it, but gives no resolution.
References
Primary source
Peter J. Cho and Keunyoung Jeong, “Average analytic rank of elliptic curves with prescribed torsion”, arXiv:2005.06862 (2021).
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