In this paper we determine the quadratic points on the modular curves 𝑋₀(𝑁), where the curve is non-hyperelliptic, the genus is 3, 4, or 5, and the Mordell–Weil group of 𝐽₀(𝑁) is finite. The ...

Let f be a newform, as specified by its Hecke eigenvalues, on a Shimura curve X. We describe a method for evaluating f. The most interesting case is when X arises as a compact quotient of the ...

An international group of mathematicians at MIT and other institutions has released a new online resource that provides detailed maps of previously uncharted mathematical terrain. The "L-functions and ...

Mathematicians from 12 countries – including one with Maltese heritage - have launched a massive database of mathematical objects including elliptic curves, and a special class of zeroes, that has ...

Dr Jarvis works in the area of algebraic number theory, an area which uses techniques from algebra, algebraic geometry and classical number theory, amongst others. In particular, he studies the ...

In August, a pair of mathematicians discovered an exotic, record-breaking curve. In doing so, they tapped into a major open question about one of the oldest and most fundamental kinds of equations in ...

Editor's note: See the original article on PurpleAlientPlanet. Some of my research is focused on the implementation issues of elliptic curve cryptography on embedded systems. Since I often have to ...

Author Nick Sullivan worked for six years at Apple on many of its most important cryptography efforts before recently joining CloudFlare, where he is a systems engineer. He has a degree in mathematics ...

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves. Elliptic curves seem to admit infinite variety, but they really only come in two flavors. That ...