Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $3^{4}\cdot6^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| 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: | 24L3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}42&5\\91&12\end{bmatrix}$, $\begin{bmatrix}44&73\\73&88\end{bmatrix}$, $\begin{bmatrix}51&56\\110&69\end{bmatrix}$, $\begin{bmatrix}76&103\\11&76\end{bmatrix}$, $\begin{bmatrix}107&68\\70&113\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.byt.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $245760$ |
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 |
|---|---|---|---|---|---|
| 24.72.1-24.be.1.11 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 120.72.1-24.be.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.72.2-120.cv.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.61 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.df.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.df.1.61 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.7-120.bgc.1.36 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.brc.1.8 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cff.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cfh.1.12 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dcu.1.14 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dcy.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ded.1.14 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.deh.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dyc.1.14 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dyf.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ebd.1.24 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ebi.1.8 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eeq.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eet.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.efv.1.15 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ega.1.3 | $120$ | $2$ | $2$ | $7$ |