Invariants
Level: | $112$ | $\SL_2$-level: | $112$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $13 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot14^{2}\cdot16\cdot28\cdot112$ | Cusp orbits | $1^{8}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 13$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 13$ | ||||||
Rational cusps: | $8$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 112C13 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}11&12\\30&57\end{bmatrix}$, $\begin{bmatrix}19&104\\12&39\end{bmatrix}$, $\begin{bmatrix}33&86\\70&73\end{bmatrix}$, $\begin{bmatrix}77&100\\22&83\end{bmatrix}$, $\begin{bmatrix}97&46\\2&53\end{bmatrix}$, $\begin{bmatrix}102&47\\107&50\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.192.13.o.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $2$ |
Cyclic 112-torsion field degree: | $48$ |
Full 112-torsion field degree: | $129024$ |
Rational points
This modular curve has 8 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 |
---|---|---|---|---|---|
56.192.5-56.bl.1.37 | $56$ | $2$ | $2$ | $5$ | $0$ |
112.192.5-56.bl.1.31 | $112$ | $2$ | $2$ | $5$ | $?$ |