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 ...

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 ...

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 ...

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 ...

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 ...

When it comes to public key cryptography, most systems today are still stuck in the 1970s. On December 14, 1977, two events occurred that would change the world: Paramount Pictures released Saturday ...

Elliptic Curve Cryptography (ECC) has emerged as a favoured approach in modern cryptography, notably due to its ability to deliver robust security with relatively small key sizes. Extensive hardware ...