Invariants
| Level: | $120$ | $\SL_2$-level: | $60$ | 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 | $6^{2}\cdot12^{2}\cdot30^{2}\cdot60^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 15$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 60A15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&40\\110&31\end{bmatrix}$, $\begin{bmatrix}13&78\\66&55\end{bmatrix}$, $\begin{bmatrix}20&59\\103&86\end{bmatrix}$, $\begin{bmatrix}44&65\\77&22\end{bmatrix}$, $\begin{bmatrix}67&114\\18&53\end{bmatrix}$, $\begin{bmatrix}90&59\\19&60\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.216.15.cgo.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| 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.ek.2.14 | $40$ | $3$ | $3$ | $3$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.216.6-30.a.2.16 | $30$ | $2$ | $2$ | $6$ | $0$ |
| 40.144.3-40.ek.2.14 | $40$ | $3$ | $3$ | $3$ | $1$ |
| 120.216.6-30.a.2.59 | $120$ | $2$ | $2$ | $6$ | $?$ |