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: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16J3 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}5&26\\32&85\end{bmatrix}$, $\begin{bmatrix}39&72\\76&97\end{bmatrix}$, $\begin{bmatrix}59&36\\36&109\end{bmatrix}$, $\begin{bmatrix}65&4\\8&77\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.3.bp.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 real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.96.2-16.d.2.9 | $16$ | $2$ | $2$ | $2$ | $0$ |
56.96.0-56.ba.1.1 | $56$ | $2$ | $2$ | $0$ | $0$ |
112.96.0-56.ba.1.6 | $112$ | $2$ | $2$ | $0$ | $?$ |
112.96.1-112.a.2.4 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.1-112.a.2.20 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.96.2-16.d.2.6 | $112$ | $2$ | $2$ | $2$ | $?$ |
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.x.1.2 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.z.1.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bh.4.2 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.br.2.15 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bv.2.8 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bw.2.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.by.2.4 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.cb.1.1 | $112$ | $2$ | $2$ | $5$ |