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Sep 17, 2021 at 17:34 comment added Will Sawin I think sublinear in $p$ is known for hyperelliptic curves, at least, by Harvey's variant of Kedlaya's $p$-adic algorithm.
Sep 17, 2021 at 17:25 history edited Steven Stadnicki CC BY-SA 4.0
Added a note about input sizes
Sep 17, 2021 at 5:36 history answered Steven Stadnicki CC BY-SA 4.0