Part (a) gives
$$
2\log H(y(P))=3\log H(x(P))+O_E(1).
$$
Thus replacing the $x$-coordinate height literally by the $y$-coordinate height multiplies the resulting canonical height by $3/2$. Multiplying the new naive height by $2/3$ restores the original normalization.


Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 125 / 4 / c / iii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-125/4/c/iii/solution