Questions tagged [j-invariant]
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8 questions with no upvoted or accepted answers
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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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Is it true that all algebraic values of the $j$-invariant have a real Galois conjugate?
This is a follow-up of my recent question on real values of the $j$-invariant. It has had a partial response so far, establishing that any "reality root" $n$ is indeed rational. Now it ...
- 13.4k
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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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Expressing modular functions of level 9 and 32 as rational functions
Let
$$\gamma_2(\tau)=j(\tau)^{1/3},\qquad \mathfrak f_1(\tau)=\frac{\eta(\tau/2)}{\eta(\tau)},$$
where $j$ is the modular invariant and $\eta$ is the Dedekind eta function. Cox in his Primes of the ...
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Zagier's algebraicity of singular moduli
Let $\mathcal M_m\subset M(2,\mathbb Z)$ be the set matrices with determinant $n$. The modular group $\Gamma$ acts on $\mathcal M_m$ from the left and we have the following finite set as a set of ...
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The value of the Hauptmodul at CM point
Let $J$ be a classical normalized $j$-invariant (that is, J=j-744).
Then, it is a classical result that $J(\tau)$ is an algebraic integer if $\tau$ is an imaginary quadratic number (that is, $a\tau^2+...
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Algebraic degrees of $j\left(\sqrt{-n}\right)$ and $j\left(\frac{1 + \sqrt{-n}}{2}\right)$ and class numbers of $Q(\sqrt{-n})$
Let $n\in\mathbb N$ be squarefree. Denote by $h(n)$ the class number of $Q(\sqrt{-n})$ and by $d_1(n)$ and $d_2(n)$ the degrees of the algebraic numbers $j\left(\sqrt{-n}\right)$ and $j\left(\frac{1 + ...
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Why the cofficients of the $j$-invariant polynomial are integers and how to compute them?
In the Page 333 of the book “Elliptic curves number theory and cryptogarphy” Lawrence C. Washington.
Given $\tau_i\in H$(up-half plane),and $j(\tau_i)$ is the j-invariant of the lattice $\mathbb Z_\...
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