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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}103&184\\214&95\end{bmatrix}$, $\begin{bmatrix}163&116\\12&31\end{bmatrix}$, $\begin{bmatrix}227&92\\164&169\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.96.1.by.2 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.i.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
232.96.0-8.i.1.3 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.k.1.6 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.k.1.13 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.l.2.2 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.l.2.10 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.z.2.2 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.z.2.10 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.1-232.bi.2.6 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bi.2.10 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bj.1.11 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bj.1.16 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bs.1.6 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bs.1.14 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |