Invariants
| Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16J3 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}9&66\\56&5\end{bmatrix}$, $\begin{bmatrix}45&90\\24&65\end{bmatrix}$, $\begin{bmatrix}109&78\\8&85\end{bmatrix}$, $\begin{bmatrix}111&66\\60&21\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.96.3.cd.1 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $16$ |
| Cyclic 112-torsion field degree: | $768$ |
| Full 112-torsion field degree: | $258048$ |
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 |
|---|---|---|---|---|---|
| 16.96.1-16.a.1.4 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 56.96.0-56.ba.1.1 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 112.96.0-56.ba.1.5 | $112$ | $2$ | $2$ | $0$ | $?$ |
| 112.96.1-16.a.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ |
| 112.96.2-112.d.2.11 | $112$ | $2$ | $2$ | $2$ | $?$ |
| 112.96.2-112.d.2.18 | $112$ | $2$ | $2$ | $2$ | $?$ |
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.y.3.4 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.ba.1.4 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bg.2.2 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.bi.2.4 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.dz.2.8 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.ea.1.3 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.ef.1.1 | $112$ | $2$ | $2$ | $5$ |
| 112.384.5-112.eg.2.15 | $112$ | $2$ | $2$ | $5$ |