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2026-02-23 12:05:44.1771848344

Why all supersingular elliptic curves over $\bar{\mathbb{F}_p}$ are isogenous?

111 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At 23 Feb 2026 - 12:05 2026-02-23 12:15:44.1771848944

Lemma 3.2.1 in Baker, González-Jiménez, González, Poonen, "Finiteness theorems for modular curves of genus at least 2", Amer. J. Math. 127 (2005), 1325–1387.
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I don't understand why "all supersingular elliptic curves over $\bar{F_p}$ are isogenous". Could anyone help me?
This problem arises from Supersingular elliptic curves and their "functorial" structure over F_p^2.
Moreover, I found some similar question: Isogenies between elliptic curves and their endomorphism rings and Isogenies between supersingular elliptic curves.

algebraic-geometry finite-fields elliptic-curves isogeny
Original Q&A

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