Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | 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: | 12V1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&12\\110&31\end{bmatrix}$, $\begin{bmatrix}13&24\\71&115\end{bmatrix}$, $\begin{bmatrix}55&12\\57&1\end{bmatrix}$, $\begin{bmatrix}67&0\\87&17\end{bmatrix}$, $\begin{bmatrix}67&36\\63&101\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.1.ru.3 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $184320$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $24$ | $24$ | $0$ | $0$ | full Jacobian |
| 40.24.0-20.h.1.2 | $40$ | $8$ | $8$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.96.0-24.bu.4.24 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.96.1-60.l.1.12 | $60$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 120.96.0-24.bu.4.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-120.ds.2.40 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-120.ds.2.61 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-60.l.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.384.5-120.zk.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.zn.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.baa.4.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bad.4.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bax.4.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bbc.4.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bbf.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bbk.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bgd.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bgi.2.24 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bgt.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bgy.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bhs.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bhv.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bia.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.bid.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |