### Abstract

Weierstrass points are special points on a Riemann surface that carry a lot of information. Ogg studied such points on X_{0}(pM) (for M such that X_{0}(M) has genus zero and p prime with p ł M), and he proved that if Q is a Q-rational Weierstrass point on X_{0}(pM), then its reduction modulo p is supersingular. The paper shows that, for square-free M on the list, all supersingular j-invariants are obtained in this way. Furthermore, for most cases where M is prime, the explicit correspondence between Weierstrass points and supersingular j-invariants in characteristic p is described. Along the way, a useful formula of Rohrlich for computing a certain Wronskian of modular forms modulo p is generalized.

Original language | English |
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Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Journal of the London Mathematical Society |

Volume | 70 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 2004 |

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### ASJC Scopus subject areas

- Mathematics(all)