Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $3136$ | ||
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 | $4^{8}\cdot8^{8}$ | 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: | 8K1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}17&40\\64&51\end{bmatrix}$, $\begin{bmatrix}89&68\\0&13\end{bmatrix}$, $\begin{bmatrix}97&4\\84&55\end{bmatrix}$, $\begin{bmatrix}103&20\\48&47\end{bmatrix}$, $\begin{bmatrix}111&32\\92&69\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.w.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $32$ |
Cyclic 112-torsion field degree: | $768$ |
Full 112-torsion field degree: | $258048$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3136.2.a.m |
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 |
---|---|---|---|---|---|---|
16.96.0-8.c.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.96.0-8.c.1.2 | $112$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.384.5-112.c.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.c.1.15 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.e.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.e.1.12 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.n.1.4 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.n.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.t.2.4 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.t.2.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.w.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.w.1.6 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.y.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.y.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.z.2.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.z.2.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.bb.1.6 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.bb.1.13 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.co.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.co.1.6 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cu.1.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cu.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.dd.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.dd.1.15 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.df.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.df.1.12 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |