Great write-up; I need to review how GRH is used to prove bounds on the rank of elliptic curves. Also, the talk about polynomial parametrizations reminded me o

Great write-up; I need to review how GRH is used to prove bounds on the rank of elliptic curves. Also, the talk about polynomial parametrizations reminded me of the first Diophantine equation I solved in high school: (a^2+b^2)/(a+b) = (c^2+d^2)/(c+d). I had initially thought it had finitely many solutions, but then Nikos Tzanakis corrected me and told me I am missing many. So I toiled for two entire days and found the complete 2-parameter polynomial family of solutions.