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Felipe Voloch
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On one hand, supersingularity is a "modular" property, i.e. a property of the elliptic curve represented by the point on the modular curve, so it should have a modular description. On the other hand, any finite set of $j$-values $j_1,\ldots,j_n$ is the set of zeros of a modular form. For example: $\Delta^n\prod(j-j_i)^{12}$$\Delta^n\prod(j-j_i)$.

On one hand, supersingularity is a "modular" property, i.e. a property of the elliptic curve represented by the point on the modular curve, so it should have a modular description. On the other hand, any finite set of $j$-values $j_1,\ldots,j_n$ is the set of zeros of a modular form. For example: $\Delta^n\prod(j-j_i)^{12}$.

On one hand, supersingularity is a "modular" property, i.e. a property of the elliptic curve represented by the point on the modular curve, so it should have a modular description. On the other hand, any finite set of $j$-values $j_1,\ldots,j_n$ is the set of zeros of a modular form. For example: $\Delta^n\prod(j-j_i)$.

Source Link
Felipe Voloch
  • 30.5k
  • 6
  • 85
  • 151

On one hand, supersingularity is a "modular" property, i.e. a property of the elliptic curve represented by the point on the modular curve, so it should have a modular description. On the other hand, any finite set of $j$-values $j_1,\ldots,j_n$ is the set of zeros of a modular form. For example: $\Delta^n\prod(j-j_i)^{12}$.