Source: cirosantilli/largest-known-ranks-of-an-elliptic-curve-over-the-rational-numbers
= Largest known ranks of an elliptic curve over the rational numbers
https://web.math.pmf.unizg.hr/~duje/tors/rankhist.html gives a list with Elkies (2006) on top with:
$$
y^2 + xy + y = x^3 - x^2 - 20067762415575526585033208209338542750930230312178956502 x + 34481611795030556467032985690390720374855944359319180361266008296291939448732243429
$$
TODO why this non standard formulation?