BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (Brown University)
DTSTART:20250915T200000Z
DTEND:20250915T210000Z
DTSTAMP:20260423T040043Z
UID:NTBU/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/27/">Ra
 tional points on $X_0(N)^∗$ when $N$ is non-squarefree</a>\nby Sachi Has
 himoto (Brown University) as part of Boston University Number Theory Semin
 ar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstract\nThe 
 rational points of the modular curve $X_0(N)$ classify pairs $(E\,C_N)$ of
  elliptic curves over $\\mathbb{Q}$ together with a rational cyclic subgro
 up of order $N$. The curve $X_0(N)^∗$ is the quotient of $X_0(N)$ by the
  full group of Atkin-Lehner involutions. Elkies showed that the rational p
 oints on this curve classify elliptic curves over the algebraic closure of
  $\\mathbb{Q}$ that are isogenous to their Galois conjugates\, and conject
 ured that when $N$ is large enough\, the points are all CM or cuspidal. In
  joint work with Timo Keller and Samuel Le Fourn\, we study the rational p
 oints on the family $X_0(N)^∗$ for $N$ non-squarefree. In particular we 
 will report on some integrality results for the j-invariants of points on 
 $X_0(N)^∗$.\n
LOCATION:https://researchseminars.org/talk/NTBU/27/
END:VEVENT
END:VCALENDAR