Oh man, this is my new favorite challenge. Thanks to ArtemisFY and jack0 for the nudges, and sampriti for creating it. I knew nothing about ECC or sage before starting this, and it was a very educational journey. Andrea Corbellini’s blog has a good “gentle introduction” to the field if you are starting from nothing. The Hankerson, Menezes, and Vanstone textbook is more comprehensive. Feel free to PM for nudges, and Merry Christmas, everybody.