Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | 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 | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
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: | 16E1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}33&24\\70&75\end{bmatrix}$, $\begin{bmatrix}43&96\\92&73\end{bmatrix}$, $\begin{bmatrix}95&24\\69&67\end{bmatrix}$, $\begin{bmatrix}103&80\\96&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.48.1.d.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $384$ |
Full 112-torsion field degree: | $516096$ |
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 |
---|---|---|---|---|---|---|
16.48.0-8.k.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.0-8.k.1.4 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.48.0-112.g.1.9 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-112.g.1.20 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.1-112.a.1.9 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.48.1-112.a.1.20 | $112$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.192.1-112.u.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.u.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.v.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.v.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.w.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.w.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.x.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.x.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |