| Curve name |
$X_{94c}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
No |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 0 \\ 12 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 12 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{94}$ |
| Curves that $X_{94c}$ minimally covers |
|
| Curves that minimally cover $X_{94c}$ |
|
| Curves that minimally cover $X_{94c}$ and have infinitely many rational
points. |
|
| Model |
$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is
given by
\[y^2 = x^3 + A(t)x + B(t), \text{ where}\]
\[A(t) = 81t^{12} + 1944t^{11} + 16416t^{10} + 43200t^{9} - 233280t^{8} -
2405376t^{7} - 9400320t^{6} - 19243008t^{5} - 14929920t^{4} + 22118400t^{3} +
67239936t^{2} + 63700992t + 21233664\]
\[B(t) = 3888t^{17} + 132192t^{16} + 1987200t^{15} + 17314560t^{14} +
95219712t^{13} + 327075840t^{12} + 572645376t^{11} - 306561024t^{10} -
3698196480t^{9} - 2452488192t^{8} + 36649304064t^{7} + 167462830080t^{6} +
390019940352t^{5} + 567363502080t^{4} + 520932556800t^{3} + 277226717184t^{2} +
65229815808t\]
|
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 14300x - 1808000$, with conductor $5600$ |
| Generic density of odd order reductions |
$9249/57344$ |