| Curve name |
$X_{92d}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 8 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{92}$ |
| Curves that $X_{92d}$ minimally covers |
|
| Curves that minimally cover $X_{92d}$ |
|
| Curves that minimally cover $X_{92d}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = -108t^{14} + 6264t^{12} - 1620t^{10} - 15984t^{8} - 1620t^{6} +
6264t^{4} - 108t^{2}\]
\[B(t) = 432t^{21} + 55728t^{19} - 285120t^{17} - 423360t^{15} + 541728t^{13} +
541728t^{11} - 423360t^{9} - 285120t^{7} + 55728t^{5} + 432t^{3}\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy + y = x^3 - x^2 + 920173x + 1174310804$, with conductor
$7605$ |
| Generic density of odd order reductions |
$25/224$ |