#### Record breaking elliptic curve!

Collaboration PI Noam Elkies and Zev Klagsbrun found the first elliptic curve defined over the rational numbers with rank at least 29. Assuming the Generalized Riemann Hypothesis, the rank is exactly 29. The previous record, with rank 28, dates from 2006. The new curve was found by a sieve search on a rank-17 elliptic fibration of a K3 surface – the same surface used to find the rank-28 curve – using the techniques described in their ANTS-XIV (2020) paper. For each specialization that was a candidate for high rank, they searched for points outside the fibration’s generic rank 17 subgroup of rational points; for the new curve this search found 12 more independent points.