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: | $3 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16H3 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}9&76\\96&27\end{bmatrix}$, $\begin{bmatrix}65&80\\62&21\end{bmatrix}$, $\begin{bmatrix}93&20\\94&99\end{bmatrix}$, $\begin{bmatrix}105&100\\68&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.3.br.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 no $\Q_p$ points for $p=29$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.96.1-8.p.1.2 | $8$ | $2$ | $2$ | $1$ | $0$ |
112.96.1-112.a.1.4 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.1-112.a.1.15 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.1-112.a.2.4 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.1-112.a.2.23 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.1-8.p.1.4 | $112$ | $2$ | $2$ | $1$ | $?$ |
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.bu.1.2 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bu.2.8 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bw.1.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bw.2.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.by.1.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.by.2.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.ca.1.2 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.ca.2.15 | $112$ | $2$ | $2$ | $5$ |