脊柱：一条超奇异高速公路
The Spine: A Supersingular Highway
AI总结：
研究超奇异\(\ell\)-同构图脊柱结构在\(\ell = 2\)且\(p = 71, 119\pmod{120}\)时的情况，通过找到相关函数求出平均直径，以此区分脊柱不同结构，为其结构随\(p\)变化行为提供启发式方法。
AI中文摘要：
我们考虑超奇异\(\ell\)-同构图的脊柱结构，针对arXiv:2502.03613未能完全描述的一种情况，即\(\ell = 2\)且\(p = 71, 119\pmod{120}\)。我们找到了脊柱各组件的距离、偏心率和直径函数，排除了不在\(\mathbb{F}_p\)上定义的非平凡边。利用这些函数，我们求出了脊柱的平均直径，并展示了该值如何区分脊柱的不同结构。这使我们能够通过显式计算为脊柱结构随\(p\)变化的行为提供启发式方法。
英文摘要：
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.
