Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}29&68\\184&145\end{bmatrix}$, $\begin{bmatrix}177&184\\42&49\end{bmatrix}$, $\begin{bmatrix}225&112\\73&231\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.48.1.eo.1 for the level structure with $-I$) |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $3360$ |
Full 232-torsion field degree: | $10913280$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.x.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
116.48.0-116.d.1.2 | $116$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0-116.d.1.6 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0-8.x.1.3 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.1-232.n.1.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.48.1-232.n.1.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |