Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | 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 | $2^{8}\cdot4^{4}\cdot16^{4}$ | 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: | 16M1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}1&56\\38&33\end{bmatrix}$, $\begin{bmatrix}65&32\\80&75\end{bmatrix}$, $\begin{bmatrix}65&80\\50&13\end{bmatrix}$, $\begin{bmatrix}89&24\\98&1\end{bmatrix}$, $\begin{bmatrix}105&72\\22&61\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.1.i.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $768$ |
Full 112-torsion field degree: | $258048$ |
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.l.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.96.0-112.d.2.1 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.d.2.2 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-8.l.1.2 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bf.2.2 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bf.2.15 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bh.2.4 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bh.2.13 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.1-112.b.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.b.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bz.2.4 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bz.2.13 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.cb.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.cb.2.15 | $112$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.384.5-112.bp.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.bq.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ck.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cl.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.er.1.2 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.es.1.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ev.1.2 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ew.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ez.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.fa.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.fd.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.fe.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |