8 papers
On superspecial hyperelliptic curves of Rosenhain forms
Ryo Ohashi
Any genus- hyperelliptic curve defined over an algebraically closed field of characteristic can be written in a Rosenhain form as $y^2 = x(x-1)\prod_{i=1}^{2g-1}(…
Superspecial plane quintics with large automorphism groups
Ryo Ohashi
In this paper, we study plane quintic curves whose automorphism groups have order greater than 10, as well as those with cyclic automorphism groups of order 8 and 10. The latter tw…
Generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians
Ryo Ohashi
Superspecial curves are important objects in number theory and algebraic geometry, and the existence in genus remains an open problem for all but finitely many character…
On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain
Ryo Ohashi, Momonari Kudo
While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 wi…
Enumeration Algorithm for Genus-4 Superspecial Hyperelliptic Curves with Automorphism Group
Takara Taniguchi, Ryo Ohashi, Tsuyoshi Takagi
In this paper, we propose an algorithm to enumerate genus-4 superspecial hyperelliptic curves whose automorphism groups isomorphic to the quaternion group. By implementing this alg…
Superspecial genus- double covers of elliptic curves
Takumi Ogasawara, Ryo Ohashi, Kosuke Sakata +1
In this paper we study genus- curves obtained as double covers of elliptic curves. Firstly we shall give explicit defining equations of such curves with explicit criterion for w…
Listing superspecial curves of genus three using Richelot isogeny graphs
Ryo Ohashi, Hiroshi Onuki, Momonari Kudo +2
In algebraic geometry, superspecial curves are important research objects. While the number of superspecial genus-3 curves in characteristic is known, the number of hyperellipt…
Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group
Ryo Ohashi, Momonari Kudo
In algebraic geometry, enumerating or finding superspecial curves in positive characteristic is important both in theory and in computation. In this paper, we propose feasible…