| Curve name |
$X_{202f}$ |
| Index |
$96$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 0 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{202}$ |
| Curves that $X_{202f}$ minimally covers |
|
| Curves that minimally cover $X_{202f}$ |
|
| Curves that minimally cover $X_{202f}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = -27648t^{16} - 3207168t^{14} - 5059584t^{12} + 4119552t^{10} -
1226880t^{8} + 1029888t^{6} - 316224t^{4} - 50112t^{2} - 108\]
\[B(t) = 1769472t^{24} - 456523776t^{22} - 5109350400t^{20} - 563576832t^{18} +
606818304t^{16} + 3849928704t^{14} - 3232051200t^{12} + 962482176t^{10} +
37926144t^{8} - 8805888t^{6} - 19958400t^{4} - 445824t^{2} + 432\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + x^2 - 58497x - 5412897$, with conductor $1344$ |
| Generic density of odd order reductions |
$271/2688$ |