| Curve name |
$X_{187l}$ |
| Index |
$96$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 4 \\ 6 & 5 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 6 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{187}$ |
| Curves that $X_{187l}$ minimally covers |
|
| Curves that minimally cover $X_{187l}$ |
|
| Curves that minimally cover $X_{187l}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = -108t^{24} - 864t^{20} - 25920t^{16} - 193536t^{12} - 414720t^{8} -
221184t^{4} - 442368\]
\[B(t) = -432t^{36} - 5184t^{32} + 207360t^{28} + 2709504t^{24} + 14598144t^{20}
+ 58392576t^{16} + 173408256t^{12} + 212336640t^{8} - 84934656t^{4} -
113246208\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + x^2 - 16033x + 356063$, with conductor $4800$ |
| Generic density of odd order reductions |
$271/2688$ |