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2
votes
Accepted
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 …
16
votes
Accepted
$j$-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 …