Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
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 | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
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: | 16M1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}1&80\\30&87\end{bmatrix}$, $\begin{bmatrix}33&0\\50&107\end{bmatrix}$, $\begin{bmatrix}53&8\\10&51\end{bmatrix}$, $\begin{bmatrix}73&48\\92&15\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.1.o.2 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $384$ |
Full 112-torsion field degree: | $258048$ |
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 |
---|---|---|---|---|---|---|
16.96.0-16.d.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.96.0-56.bb.1.1 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.96.0-16.d.1.12 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-56.bb.1.1 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bl.2.7 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bl.2.10 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.br.1.8 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.br.1.9 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.1-112.a.2.4 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.a.2.11 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.1.8 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.1.9 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bv.2.7 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bv.2.10 | $112$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.384.5-112.bh.2.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.by.2.4 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ee.2.4 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.ej.2.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |