## The modular curve $X_{207}$

Curve name $X_{207}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$ $8$ $24$ $X_{92}$
Meaning/Special name
Chosen covering $X_{92}$
Curves that $X_{207}$ minimally covers $X_{92}$, $X_{120}$, $X_{122}$
Curves that minimally cover $X_{207}$ $X_{476}$, $X_{478}$, $X_{479}$, $X_{487}$, $X_{521}$, $X_{527}$, $X_{529}$, $X_{531}$, $X_{207a}$, $X_{207b}$, $X_{207c}$, $X_{207d}$, $X_{207e}$, $X_{207f}$, $X_{207g}$, $X_{207h}$, $X_{207i}$, $X_{207j}$, $X_{207k}$, $X_{207l}$, $X_{207m}$, $X_{207n}$
Curves that minimally cover $X_{207}$ and have infinitely many rational points. $X_{207a}$, $X_{207b}$, $X_{207c}$, $X_{207d}$, $X_{207e}$, $X_{207f}$, $X_{207g}$, $X_{207h}$, $X_{207i}$, $X_{207j}$, $X_{207k}$, $X_{207l}$, $X_{207m}$, $X_{207n}$
Model $\mathbb{P}^{1}, \mathbb{Q}(X_{207}) = \mathbb{Q}(f_{207}), f_{92} = \frac{f_{207}^{2} - 8}{f_{207}^{2} + 8f_{207} + 8}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + 153667x + 1050376556$, with conductor $25410$
Generic density of odd order reductions $17/168$