Invariants
| Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{4}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16I2 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}41&8\\0&25\end{bmatrix}$, $\begin{bmatrix}47&20\\52&3\end{bmatrix}$, $\begin{bmatrix}49&32\\76&93\end{bmatrix}$, $\begin{bmatrix}89&80\\108&1\end{bmatrix}$, $\begin{bmatrix}105&12\\68&75\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.96.2.d.1 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $32$ |
| Cyclic 112-torsion field degree: | $768$ |
| Full 112-torsion field degree: | $258048$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.96.0-8.c.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 112.96.0-8.c.1.2 | $112$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 112.384.5-112.p.1.1 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.p.2.15 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.t.1.11 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.t.2.4 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bo.1.1 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bo.5.21 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bs.1.3 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bs.2.13 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.cx.1.9 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.cx.2.8 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.cz.1.19 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.cz.2.9 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.dd.1.7 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.dd.2.9 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.dh.1.3 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.dh.2.13 | $112$ | $2$ | $2$ | $5$ |
| 112.384.7-112.l.1.12 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.n.1.15 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.q.1.19 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.t.1.15 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.bc.1.7 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.bd.1.4 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.bh.1.7 | $112$ | $2$ | $2$ | $7$ |
| 112.384.7-112.bj.1.10 | $112$ | $2$ | $2$ | $7$ |