| Curve name |
$X_{60}$ |
| Index |
$24$ |
| Level |
$4$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
| Level | Index of image | Corresponding curve |
| $2$ |
$3$ |
$X_{6}$ |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{23}$ |
| Curves that $X_{60}$ minimally covers |
$X_{20}$, $X_{23}$, $X_{26}$, $X_{27}$ |
| Curves that minimally cover $X_{60}$ |
$X_{277}$, $X_{278}$, $X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$ |
| Curves that minimally cover $X_{60}$ and have infinitely many rational
points. |
$X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{60}) = \mathbb{Q}(f_{60}), f_{23} =
\frac{f_{60}^{2} + \frac{1}{2}}{f_{60}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + 117x + 918$, with conductor $360$ |
| Generic density of odd order reductions |
$13/84$ |