CoCalc Public Fileswww / talks / IDA-10-2000 / www / text24.htmOpen with one click!
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
Slide 25
First page Back Continue Last page Summary Graphics

Applications of Modular Symbols

  • Enumerating all elliptic curves of conductor N.

  • Computing a basis of modular forms of given weight and level.

  • Proving theorems towards the BSD conjecture; e.g., that L(E,1)/Omega is a rational number.

  • Computing the modular degree. Understanding the modular degree well <==> ABC conjecture.

  • Loic Merel's "Uniform boundedness theorem".