13 citations · 24 across the 7 of their papers we have counts for
7 papers · 1 filter
Quadratic points on
Philippe Michaud-Jacobs, Filip Najman
We determine all the quadratic points on the genus modular curve , thus completing the answer to a recent question of Banwait, the second-named author, and Padurariu…
Computing quadratic points on modular curves
Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs +3
In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N…
Computing points on bielliptic modular curves over fixed quadratic fields
Philippe Michaud-Jacobs
We present a Mordell-Weil sieve that can be used to compute points on certain bielliptic modular curves over fixed quadratic fields. We study $X_0(N)(\mathbb{Q}(\sqrt{d}))…
Mazur's isogeny theorem
Philippe Michaud-Jacobs
Mazur's isogeny theorem states that if is a prime for which there exists an elliptic curve that admits a rational isogeny of degree , then $p \in \{2,3,5,7,…
On elliptic curves with -isogenies over quadratic fields
Philippe Michaud-Jacobs
Let be a number field. For which primes does there exist an elliptic curve admitting a -rational -isogeny? Although we have an answer to this question over th…
On some Generalized Fermat Equations of the form
Philippe Michaud-Jacobs
The primary aim of this paper is to study the generalized Fermat equation \[ x^2+y^{2n} = z^{3p} \] in coprime integers , , and , where and is a fixed prime…
Fermat's Last Theorem and modular curves over real quadratic fields
Philippe Michaud-Jacobs
In this paper we study the Fermat equation over quadratic fields for squarefree with . By studying quadratic points on t…