Parametrization of The Modular Curve
When n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18, or 25, X0(n) has genus zero, and hence can be parametrized by rational functions. The simplest nontrivial example is X0(2), where if
is (up to the constant term) the McKay–Thompson series for the class 2B of the Monster, and η is the Dedekind eta function, then
parametrizes X0(2) in terms of rational functions of j2. It is not necessary to actually compute j2 to use this parametrization; it can be taken as an arbitrary parameter.
Read more about this topic: Classical Modular Curve
Famous quotes containing the word curve:
“Nothing ever prepares a couple for having a baby, especially the first one. And even baby number two or three, the surprises and challenges, the cosmic curve balls, keep on coming. We can’t believe how much children change everything—the time we rise and the time we go to bed; the way we fight and the way we get along. Even when, and if, we make love.”
—Susan Lapinski (20th century)