14 citations · 29 across the 16 of their papers we have counts for
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Modularity of elliptic curves over cyclotomic -extensions of real quadratic fields
Sho Yoshikawa
We prove that all elliptic curves defined over the cyclotomic -extension of a real quadratic field are modular under the assumption that the algebraic part of the cen…
The modularity of elliptic curves over all but finitely many totally real fields of degree 5
Yasuhiro Ishitsuka, Tetsushi Ito, Sho Yoshikawa
We study the finiteness of low degree points on certain modular curves and their Atkin--Lehner quotients, and, as an application, prove the modularity of elliptic curves over all b…
Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7
Sho Yoshikawa
This version improves the old version entitled "On the modularity of elliptic curves with a residually irreducible representation". Let be an elliptic curve over an abelian tot…
On the modularity of elliptic curves over a composite field of some real quadratic fields
Sho Yoshikawa
Let be a composite field of some real quadratic fields. We give a sufficient condition on such that all elliptic curves over is modular.
The 12-th roots of the discriminant of an elliptic curve and the torsion points
Kohei Fukuda, Sho Yoshikawa
Given an elliptic curve over a field of characteristic different from 2,3, its discriminant defines a -torsor over the field. In this paper, we give an explicit description…