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math.NT2021
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…
math.NT2021
The arithmetic of a twist of the Fermat quartic
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We study the arithmetic of the twist of the Fermat quartic defined by which has no -rational point. We calculate the Mordell--Weil group of the Ja…