| Curve name |
$X_{95h}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 12 & 3 \end{matrix}\right],
\left[ \begin{matrix} 11 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 9 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{95}$ |
| Curves that $X_{95h}$ minimally covers |
|
| Curves that minimally cover $X_{95h}$ |
|
| Curves that minimally cover $X_{95h}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = -108t^{18} + 20736t^{14} + 718848t^{10} + 5308416t^{6} - 7077888t^{2}\]
\[B(t) = 432t^{27} + 248832t^{23} + 7630848t^{19} - 1953497088t^{11} -
16307453952t^{7} - 7247757312t^{3}\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 6843351x - 12841360720$, with conductor $968256$ |
| Generic density of odd order reductions |
$9249/57344$ |