Peter Bruin

activity

20102023

X_{0} (n)

and isogenies of elliptic curves over quadratic fields

30 citations · 88 across the 16 of their papers we have counts for

collaborators

Showing 2014Show all

2 papers · 1 filter

math.NT2014★ 30 cited

Hyperelliptic modular curves $X_{0} (n)$ and isogenies of elliptic curves over quadratic fields

Peter Bruin, Filip Najman

Let $n$ be an integer such that the modular curve $X_{0} (n)$ is hyperelliptic of genus $\geq 2$ and such that the Jacobian of $X_{0} (n)$ has rank $0$ over $Q$ . We determine all p…

math.AG2014★ 24 cited

Polynomial bounds for Arakelov invariants of Belyi curves

Ariyan Javanpeykar, Peter Bruin

We explicitly bound the Faltings height of a curve over Q polynomially in its Belyi degree. Similar bounds are proven for three other Arakelov invariants: the discriminant, Falting…

Hyperelliptic modular curves X0​(n) and isogenies of elliptic curves over quadratic fields

Polynomial bounds for Arakelov invariants of Belyi curves

Hyperelliptic modular curves $X_{0} (n)$ and isogenies of elliptic curves over quadratic fields