Invariants
| Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
Level structure
| $\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}85&108\\206&73\end{bmatrix}$, $\begin{bmatrix}191&40\\64&49\end{bmatrix}$, $\begin{bmatrix}219&200\\118&155\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 232.96.1.bx.1 for the level structure with $-I$) |
| Cyclic 232-isogeny field degree: | $60$ |
| Cyclic 232-torsion field degree: | $3360$ |
| Full 232-torsion field degree: | $5456640$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.96.0-8.h.1.8 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 232.96.0-8.h.1.6 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.n.2.6 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.n.2.10 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.p.2.5 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.p.2.16 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.ba.1.4 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.0-232.ba.1.10 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 232.96.1-232.bd.2.9 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 232.96.1-232.bd.2.14 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 232.96.1-232.bf.2.12 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 232.96.1-232.bf.2.14 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 232.96.1-232.bt.1.4 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 232.96.1-232.bt.1.5 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |