Invariants
| Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $2^{4}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8A5 |
Level structure
| $\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}65&230\\136&103\end{bmatrix}$, $\begin{bmatrix}93&158\\204&115\end{bmatrix}$, $\begin{bmatrix}129&106\\80&155\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 232.192.5.w.1 for the level structure with $-I$) |
| Cyclic 232-isogeny field degree: | $60$ |
| Cyclic 232-torsion field degree: | $1680$ |
| Full 232-torsion field degree: | $2728320$ |
Rational points
This modular curve has no $\Q_p$ points for $p=5$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.192.3-8.i.1.1 | $8$ | $2$ | $2$ | $3$ | $0$ |
| 232.192.1-232.l.1.7 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.1-232.l.1.11 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.1-232.w.1.1 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.1-232.w.1.9 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.1-232.w.2.5 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.1-232.w.2.10 | $232$ | $2$ | $2$ | $1$ | $?$ |
| 232.192.3-8.i.1.4 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.r.1.7 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.r.1.15 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.r.2.2 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.r.2.4 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.t.1.3 | $232$ | $2$ | $2$ | $3$ | $?$ |
| 232.192.3-232.t.1.4 | $232$ | $2$ | $2$ | $3$ | $?$ |