| Curve name |
$X_{94d}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 5 \\ 4 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{94}$ |
| Curves that $X_{94d}$ minimally covers |
|
| Curves that minimally cover $X_{94d}$ |
|
| Curves that minimally cover $X_{94d}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = 324t^{8} + 5184t^{7} + 13824t^{6} - 124416t^{5} - 732672t^{4} -
995328t^{3} + 884736t^{2} + 2654208t + 1327104\]
\[B(t) = 31104t^{11} + 684288t^{10} + 5446656t^{9} + 15925248t^{8} -
14598144t^{7} - 167215104t^{6} - 116785152t^{5} + 1019215872t^{4} +
2788687872t^{3} + 2802843648t^{2} + 1019215872t\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 572x + 14464$, with conductor $1120$ |
| Generic density of odd order reductions |
$307/2688$ |