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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}17&228\\12&109\end{bmatrix}$, $\begin{bmatrix}33&100\\164&31\end{bmatrix}$, $\begin{bmatrix}113&52\\120&17\end{bmatrix}$, $\begin{bmatrix}121&228\\136&159\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.96.1.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: | $5456640$ |
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.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
232.96.0-8.c.1.6 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.b.1.11 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.b.1.17 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.s.1.1 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.s.1.12 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.t.1.1 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.0-232.t.1.12 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.96.1-232.n.2.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.n.2.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bi.2.14 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bi.2.15 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bj.2.5 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.96.1-232.bj.2.16 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
232.384.5-232.w.1.2 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.384.5-232.y.1.1 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.384.5-232.z.2.3 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.384.5-232.bb.1.1 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |