| Curve name |
$X_{94f}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 5 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 4 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{94}$ |
| Curves that $X_{94f}$ minimally covers |
|
| Curves that minimally cover $X_{94f}$ |
|
| Curves that minimally cover $X_{94f}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = 81t^{8} + 1296t^{7} + 3456t^{6} - 31104t^{5} - 183168t^{4} -
248832t^{3} + 221184t^{2} + 663552t + 331776\]
\[B(t) = 3888t^{11} + 85536t^{10} + 680832t^{9} + 1990656t^{8} - 1824768t^{7} -
20901888t^{6} - 14598144t^{5} + 127401984t^{4} + 348585984t^{3} + 350355456t^{2}
+ 127401984t\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 143x + 1808$, with conductor $2240$ |
| Generic density of odd order reductions |
$419/2688$ |