Modular curves, invariant theory and E₈
classification
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math.AGmath.RT
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modularconstructioncurvegivesinvariantlatticeroottheory
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The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by the invariant theory for the simple group $\text{PSL}(2, 13)$. This gives a different construction of the $E_8$ root lattice. It also gives an explicit construction of the modular curve $X(13)$.
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