Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | 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: | $12$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $1^{2}\cdot2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}6&77\\67&80\end{bmatrix}$, $\begin{bmatrix}16&101\\63&2\end{bmatrix}$, $\begin{bmatrix}75&118\\28&105\end{bmatrix}$, $\begin{bmatrix}101&72\\62&31\end{bmatrix}$, $\begin{bmatrix}104&85\\113&84\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.3.sn.4 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.96.0-12.c.3.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 120.96.0-12.c.3.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.96.1-120.zx.1.20 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.1-120.zx.1.61 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.2-120.h.2.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.h.2.53 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.384.5-120.ly.3.16 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.rh.3.4 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.ta.1.8 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.te.4.6 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.wq.3.6 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.xa.4.6 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.xs.2.8 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.xx.4.6 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bab.3.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bae.3.7 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bak.3.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bal.1.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bbx.4.4 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bca.4.14 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bde.4.4 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bdf.3.4 | $120$ | $2$ | $2$ | $5$ |