Invariants
| Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16A1 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}58&41\\83&52\end{bmatrix}$, $\begin{bmatrix}60&53\\97&0\end{bmatrix}$, $\begin{bmatrix}67&92\\88&7\end{bmatrix}$, $\begin{bmatrix}96&109\\5&0\end{bmatrix}$, $\begin{bmatrix}101&74\\66&85\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.24.1.b.1 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $16$ |
| Cyclic 112-torsion field degree: | $384$ |
| Full 112-torsion field degree: | $1032192$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 56.24.0-8.n.1.10 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 112.96.1-112.b.2.10 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.f.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.h.1.4 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.j.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bw.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bw.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bx.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bx.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.by.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.by.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bz.1.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.bz.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.ca.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.ca.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cb.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cb.2.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cc.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cc.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cd.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cd.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.ce.1.10 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.ch.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.ci.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.96.1-112.cl.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 112.384.13-112.l.1.13 | $112$ | $8$ | $8$ | $13$ | $?$ | not computed |