Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ | Cusp orbits | $1^{4}\cdot2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AH9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&82\\72&103\end{bmatrix}$, $\begin{bmatrix}13&86\\28&9\end{bmatrix}$, $\begin{bmatrix}31&102\\0&43\end{bmatrix}$, $\begin{bmatrix}39&26\\104&3\end{bmatrix}$, $\begin{bmatrix}79&54\\100&77\end{bmatrix}$, $\begin{bmatrix}89&54\\80&79\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.9.jl.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $92160$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal 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 |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
| 40.96.1-40.bf.2.14 | $40$ | $4$ | $4$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.43 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 40.96.1-40.bf.2.14 | $40$ | $4$ | $4$ | $1$ | $1$ |
| 120.192.3-24.bq.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ew.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ew.1.100 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.5-120.c.1.25 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.192.5-120.c.1.32 | $120$ | $2$ | $2$ | $5$ | $?$ |