论文标题
列举列出属于超专业的howe曲线$ 4 $
Algorithm to enumerate superspecial Howe curves of genus $4$
论文作者
论文摘要
Howe曲线是$ 4 $ $ 4 $的曲线，该曲线以$ \ mathbf {p}^1 $的两个椭圆形曲线的价格获得。任何Howe曲线都是规范的。本文提供了一种有效的算法，以找到超专门的how曲线和列举其同构类别的曲线。我们不仅讨论了测试超级专业性的算法，还讨论了用于测试Howe曲线同构的算法。迄今为止，对于一般规范曲线，我们的算法比作者提出的传统算法要高得多。我们显示了特征性$ 7 <p \ le 331 $中的超专门Howe曲线的存在，并通过在计算机代数系统岩浆上执行我们的算法，列举了特征性$ p \ le 53 $的同构类别的superspecial howe曲线。
A Howe curve is a curve of genus $4$ obtained as the fiber product over $\mathbf{P}^1$ of two elliptic curves. Any Howe curve is canonical. This paper provides an efficient algorithm to find superspecial Howe curves and that to enumerate their isomorphism classes. We discuss not only an algorithm to test the superspeciality but also an algorithm to test isomorphisms for Howe curves. Our algorithms are much more efficient than conventional ones proposed by the authors so far for general canonical curves. We show the existence of a superspecial Howe curve in characteristic $7<p\le 331$ and enumerate the isomorphism classes of superspecial Howe curves in characteristic $p\le 53$, by executing our algorithms over the computer algebra system Magma.
