Invariants
| Level: | $120$ | $\SL_2$-level: | $60$ | Newform level: | $300$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{6}\cdot30^{6}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30A15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&66\\72&109\end{bmatrix}$, $\begin{bmatrix}1&78\\4&71\end{bmatrix}$, $\begin{bmatrix}19&116\\52&21\end{bmatrix}$, $\begin{bmatrix}47&46\\18&97\end{bmatrix}$, $\begin{bmatrix}57&38\\4&107\end{bmatrix}$, $\begin{bmatrix}57&68\\16&53\end{bmatrix}$, $\begin{bmatrix}115&96\\52&5\end{bmatrix}$, $\begin{bmatrix}119&46\\48&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 30.240.15.a.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=53$, and therefore no 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 |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $120$ | $60$ | $0$ | $0$ |
| 40.120.3-10.a.1.2 | $40$ | $4$ | $4$ | $3$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.3-10.a.1.2 | $40$ | $4$ | $4$ | $3$ | $0$ |
| 120.48.0-6.a.1.7 | $120$ | $10$ | $10$ | $0$ | $?$ |