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Idoneal
Idoneal
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Selmer's curve $3X^3+4y^3+5z^3=0$ is an examplea non-example (see the comment below) but somwhat relevant. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY. I don't know how he obtains the equations of the companions. I hope someone can explain this.

Selmer's curve $3X^3+4y^3+5z^3=0$ is an example. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY. I don't know how he obtains the equations of the companions. I hope someone can explain this.

Selmer's curve $3X^3+4y^3+5z^3=0$ is a non-example (see the comment below) but somwhat relevant. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY.

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Idoneal
Idoneal
  • 1.7k
  • 13
  • 22

Selmer's curve $3X^3+4y^3+5z^3=0$ is an example. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY. I don't know how he obtains the equations of the companions. I hope someone can explain this.