| 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 |
|
| 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 |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{207}) = \mathbb{Q}(f_{207}), f_{92} =
\frac{f_{207}^{2} - 8}{f_{207}^{2} + 8f_{207} + 8}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| 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 |
$17/168$ |