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Fungrim entry: 441301

#solutionsτF[j(τ)=z]=1\# \mathop{\operatorname{solutions}\,}\limits_{\tau \in \mathcal{F}} \left[j(\tau) = z\right] = 1
Assumptions:zCz \in \mathbb{C}
TeX:
\# \mathop{\operatorname{solutions}\,}\limits_{\tau \in \mathcal{F}} \left[j(\tau) = z\right] = 1

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Cardinality#S\# S Set cardinality
SolutionssolutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x) Solution set
ModularJj(τ)j(\tau) Modular j-invariant
ModularGroupFundamentalDomainF\mathcal{F} Fundamental domain for action of the modular group
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("441301"),
    Formula(Equal(Cardinality(Solutions(Brackets(Equal(ModularJ(tau), z)), ForElement(tau, ModularGroupFundamentalDomain))), 1)),
    Variables(z),
    Assumptions(Element(z, CC)))

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2020-08-27 09:56:25.682319 UTC