Invariants
| Level: | $128$ | $\SL_2$-level: | $128$ | Newform level: | $1$ | ||
| Index: | $49152$ | $\PSL_2$-index: | $24576$ | ||||
| Genus: | $1857 = 1 + \frac{ 24576 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 384 }{2}$ | ||||||
| Cusps: | $384$ (none of which are rational) | Cusp widths | $64^{384}$ | Cusp orbits | $4^{4}\cdot8^{8}\cdot16^{3}\cdot64^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $244 \le \gamma \le 3712$ | ||||||
| $\overline{\Q}$-gonality: | $244 \le \gamma \le 1857$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Level structure
| $\GL_2(\Z/128\Z)$-generators: | $\begin{bmatrix}14&69\\17&74\end{bmatrix}$, $\begin{bmatrix}69&100\\20&21\end{bmatrix}$, $\begin{bmatrix}119&30\\102&63\end{bmatrix}$, $\begin{bmatrix}126&55\\123&82\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 128.24576.1857.bou.1 for the level structure with $-I$) |
| Cyclic 128-isogeny field degree: | $4$ |
| Cyclic 128-torsion field degree: | $128$ |
| Full 128-torsion field degree: | $2048$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3,5,7,\ldots,2297$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 128.24576.897-64.ix.1.2 | $128$ | $2$ | $2$ | $897$ | $?$ |
| 128.24576.897-64.ix.1.4 | $128$ | $2$ | $2$ | $897$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 128.98304.3713-128.nx.1.1 | $128$ | $2$ | $2$ | $3713$ |
| 128.98304.3713-128.nx.2.7 | $128$ | $2$ | $2$ | $3713$ |
| 128.98304.3713-128.nx.3.4 | $128$ | $2$ | $2$ | $3713$ |
| 128.98304.3713-128.nx.4.12 | $128$ | $2$ | $2$ | $3713$ |
| 128.98304.3841-128.zo.1.3 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.zy.1.5 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bdq.1.2 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bdq.2.6 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bdq.3.4 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bdq.4.8 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bee.1.1 | $128$ | $2$ | $2$ | $3841$ |
| 128.98304.3841-128.bek.1.7 | $128$ | $2$ | $2$ | $3841$ |