On Atkin-Lehner quotients of Shimura curves

Bruce W. Jordan, Ron Livné

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study the Čerednik-Drinfeld p-adic uniformization of certain Atkin-Lehner quotients of Shimura curves over ℚ. We use it to determine over which local fields they have rational points and divisors of a given degree. Using a criterion of Poonen and Stoll, we show that the Shafarevich-Tate group of their jacobians is not of square order for infinitely many cases.

Original languageAmerican English
Pages (from-to)681-685
Number of pages5
JournalBulletin of the London Mathematical Society
Issue number6
StatePublished - Nov 1999


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