| Curve name |
$X_{21}$ |
| Index |
$8$ |
| Level |
$4$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 1 \\ 3 & 0 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}\right]$ |
| Images in lower levels |
| Level | Index of image | Corresponding curve |
| $2$ |
$2$ |
$X_{2}$ |
|
| Meaning/Special name |
$X_{ns}(4)$ |
| Chosen covering |
$X_{7}$ |
| Curves that $X_{21}$ minimally covers |
$X_{2}$, $X_{7}$ |
| Curves that minimally cover $X_{21}$ |
$X_{59}$ |
| Curves that minimally cover $X_{21}$ and have infinitely many rational
points. |
|
| Model |
A model was not computed. This curve is a conic with no rational
points. |
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
None |
| Generic density of odd order reductions |
N/A |