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arXiv · 2607.14572

The Spine: A Supersingular Highway

Taha Hedayat·Renate Scheidler·Sarah Arpin
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Abstract

We consider the structure of the spine of the supersingular $\ell$-isogeny graph for one of the cases which arXiv:2502.03613 was not able to fully describe, $\ell = 2$ and $p = 71, 119\pmod{120}$. We find the distance, eccentricity, and diameter functions, of the components of the spine without the non-trivial edge not defined over $\mathbb{F}_p$. Using these functions, we find the mean diameter of the spine and show how this value distinguishes the different structures of the spine. Thus, allowing us to use explicit computations to provide heuristics on the behavior of the spine's structure as $p$ varies.

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Taha Hedayat, Renate Scheidler, Sarah Arpin. 2026-07-16. The Spine: A Supersingular Highway. https://arxiv.org/abs/2607.14572

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