# Questions tagged [j-invariant]

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### strange factorization of a simple combination of j-invariant coefficients

I am just curious: is it accidental that $744^2+744\cdot 3-196884\cdot2=162000$ has only the small primes $2$, $3$ and $5$ in its factorization?
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### Questions on the $j$-invariant

The j-invariant as a modular function is typically defined $$j(\tau) = \frac{E_4(\tau)^3}{\Delta(\tau)}$$ since $E_4$ is a modular form of weight 4 and $\Delta$ has weight 12, it follows that $j$ is a ...
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### Geometric interpretation of j-invariants of supersingular elliptic curves

In the classical theory of Complex Multiplication, one considers elliptic curves with an endomorphism ring larger than the integers. In this theory, it's possible to determine the j-invariants of all ...
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### The degree of the cube root of the $j$-invariant

I have a question which is fairly elementary, but first I must provide relevant context. Without it, my question would seem rather arbitrary and scarcely interesting. Note also that my question can be ...
I'm currently writing my master thesis about the j-invariant and his q-expansion. Now i have the result that the growth of the coefficients is asymptotically $$c(n) \sim \frac{e^{4\pi \sqrt{n}}}{\... 1 vote 1 answer 148 views ### From an eigenfom with \mathbf{Q}-coefficients to j-invariants Given a cuspidal, classical eigenform f\in S_2(\Gamma_0(N)) of weight 2 and with \mathbf{Q}-coefficients is there a way of describing the set J_f of j-invariants of the elliptic curves lying ... 12 votes 3 answers 2k views ### j-invariants of elliptic curves over finite fields Let K be a finite field, and \overline{K} its algebraic closure. It is well known that two curves are isomorphic over \overline{K} if and only if they have the same j-invariant. If two such ... 52 votes 1 answer 5k views ### There's something strange about \sqrt{\big(j(\tau)-1728\big)d} Given discriminant d and j-function j(\tau), I was looking at,$$F(\tau) = \sqrt{\big(j(\tau)-1728\big)d} which appears in Ramanujan-type pi formulas. Let $C_d$ be the odd prime factors of the ...
I learned of the following example in a recent seminar: if $j(\tau)$ denotes the usual $j$-invariant, and $\alpha = (-1+i\sqrt{163})/2$, then \begin{align*} \frac{j(i)}{1728} &= 1 \\ \frac{-j(\...