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Applications of Modular Symbols
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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".