Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1568$ | ||
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: | $\begin{bmatrix}49&72\\96&53\end{bmatrix}$, $\begin{bmatrix}65&16\\24&91\end{bmatrix}$, $\begin{bmatrix}79&64\\108&63\end{bmatrix}$, $\begin{bmatrix}81&4\\16&77\end{bmatrix}$, $\begin{bmatrix}105&80\\36&59\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.x.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $32$ |
Cyclic 112-torsion field degree: | $384$ |
Full 112-torsion field degree: | $258048$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 1568.2.a.e |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
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.1.1 | $16$ | $2$ | $2$ | $0$ | $0$ | 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.a.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.a.1.10 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.g.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.g.1.11 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.p.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.p.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.r.1.2 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.r.1.6 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.x.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.x.1.10 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.y.2.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.y.2.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.ba.2.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.ba.2.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.bb.3.10 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-56.bb.3.12 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cq.1.2 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cq.1.6 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cs.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.cs.1.5 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.db.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.db.1.11 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.dh.1.9 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.dh.1.11 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |