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: | 16G1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}38&13\\13&78\end{bmatrix}$, $\begin{bmatrix}50&93\\111&52\end{bmatrix}$, $\begin{bmatrix}80&35\\5&2\end{bmatrix}$, $\begin{bmatrix}93&30\\8&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.48.1.cd.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 no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
16.48.0-16.f.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.0-56.bv.1.5 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.48.0-16.f.1.3 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-56.bv.1.1 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.1-112.b.1.9 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.48.1-112.b.1.10 | $112$ | $2$ | $2$ | $1$ | $?$ | 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.r.2.7 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bb.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bq.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ca.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.dn.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.dy.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ec.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ep.2.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |