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Asymptotic Formula of the coefficients of the q-expansion of the J-Invariant

There are lots of reasons why it's interesting to know the growth rate of modular functions. For the $j$-invariant, the coefficients are closely related to the dimensions of the irreducible representa …
Joe Silverman's user avatar
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$j$-invariants of elliptic curves over finite fields

As Chris and Rene said, your second question is all about twists. See specifically The Arithmetic of Elliptic Curves (Springer), Proposition X.5.4, which says that if the characteristic of $K$ is not …
Joe Silverman's user avatar