All page/line numbers below refer to the published version at https://doi.org/10.1017/fms.2022.38
Page 9 line 1: "hgu \mapsto hg\chi_N(\sigma)u" should be "HgU(N) \mapsto Hg\chi_H(\sigma)U(N)"
Page 9 line 1: "[DR73, IV-5.3]" should be "[DR73, VI-5.3]"
Page 9 line 7: "that contain a conjugate of" should be "fixed by the action of".
Page 13 displayed equation (5.1): "j(E)\in k" should be "j(E)\in \mathbb{F}_q"
Page 34: The totals listed in the "SW" line of the first part of Table 9 are incorrect due to double counting 312435 elliptic curves of prime conductor that are included in two parts of the Stein-Watkins database. The Stein-Watkins database contains all elliptic curves over Q of absolute discriminant at most 10^12 that have c6-invariant of absolute value at most 1.44*10^12 whose conductor N meets either of the following criteria (which are not mutually exclusive): (1) N <= 10^8, (2) N <= 10^10 is prime. This line of the table has been updated in the most recent arXiv updated to include only curves that satisify (1), in which case the counts in the row labelled SW in the first part of the table are
SW & 35585316 & 3671438 & 181222 & 43966 & 2048 & 7444 & 368 & 1024 & 97776484 & 136789294
The counts in the second part of the table are the same (none of the double-counted curves are non-surjective at more than one prime).
Page 43: In the last sentence of the statement of Proposition A.6, "and conductor of modulus N" should be replaced by "and character of conductor dividing N".
Page 62: In reference SW02 the book title "Algorithmic Number Theory Symposium (ANTS I)" should be "Algorithmic Number Theory 5th International Symposium (ANTS V)".