Pages 5–7, Theorem 5.11 and Theorems 5.13/5.15: quotient by a finite subgroup and Vélu coordinate sums and formulas. Pages 10–11, Lemma 5.20 and Theorem 5.21: initial division polynomials, parity and multiplication coordinates. The lecture explicitly distinguishes geometric kernel points from inseparable degree and restricts short Weierstrass formulas away from characteristics two and three. The author is printed on the first-page footer.

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