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SUMMARY:Momonari Kudo (Kobe City College of Technology)\, Shushi Harashita
  (Yokohama National University)\, and Everett Howe
DTSTART:20200630T004500Z
DTEND:20200630T011500Z
DTSTAMP:20260423T200032Z
UID:ANTS14/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/5/">A
 lgorithms to enumerate superspecial Howe curves of genus four</a>\nby Momo
 nari Kudo (Kobe City College of Technology)\, Shushi Harashita (Yokohama N
 ational University)\, and Everett Howe as part of Algorithmic Number Theor
 y Symposium (ANTS XIV)\n\n\nAbstract\nA Howe curve (so named by Senda and 
 the first two authors) is a curve of genus $4$ obtained as the fiber produ
 ct of two genus-$1$ double covers of ${\\mathbf P}^1$. In this paper\, we 
 present a simple algorithm for testing isomorphism of Howe curves\, and we
  propose two main algorithms for finding and enumerating these curves: One
  involves solving multivariate systems coming from Cartier--Manin matrices
 \, while the other uses Richelot isogenies of curves of genus $2$. Compari
 ng the two algorithms by implementation and by complexity analyses\, we co
 nclude that the latter enumerates curves more efficiently. However\, in or
 der to say that the latter strategy outputs all superspecial Howe curves\,
  we require a conjecture that all superspecial curves of genus $2$ in char
 acteristic $p>2$ are connected by a path of Richelot isogenies. Given a pr
 ime $p$\, the algorithm verifies this conjecture before producing output.\
 n\nThe slides used in the pre-recorded video can be found <a href="https:/
 /math.mit.edu/~drew/ANTSXIV/SuperspecialHoweCurvesVideoSlides.pdf">here</a
 >.\n\nChairs: Brendan Creutz and Felipe Voloch\n
LOCATION:https://researchseminars.org/talk/ANTS14/5/
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