Invariants
| Level: | $120$ | $\SL_2$-level: | $120$ | Newform level: | $1$ | ||
| Index: | $432$ | $\PSL_2$-index: | $216$ | ||||
| Genus: | $15 = 1 + \frac{ 216 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $3^{2}\cdot6\cdot15^{2}\cdot24\cdot30\cdot120$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 15$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 15$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 120F15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&8\\92&1\end{bmatrix}$, $\begin{bmatrix}48&89\\47&90\end{bmatrix}$, $\begin{bmatrix}60&17\\49&48\end{bmatrix}$, $\begin{bmatrix}63&16\\110&69\end{bmatrix}$, $\begin{bmatrix}94&109\\31&92\end{bmatrix}$, $\begin{bmatrix}100&103\\103&80\end{bmatrix}$, $\begin{bmatrix}108&43\\107&24\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.216.15.jq.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $8$ |
| Cyclic 120-torsion field degree: | $256$ |
| Full 120-torsion field degree: | $81920$ |
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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $144$ | $72$ | $0$ | $0$ |
| 40.144.3-40.cg.1.25 | $40$ | $3$ | $3$ | $3$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.144.3-40.cg.1.25 | $40$ | $3$ | $3$ | $3$ | $0$ |
| 60.216.7-60.c.1.8 | $60$ | $2$ | $2$ | $7$ | $0$ |
| 120.72.2-24.cw.1.14 | $120$ | $6$ | $6$ | $2$ | $?$ |
| 120.216.7-60.c.1.70 | $120$ | $2$ | $2$ | $7$ | $?$ |