Invariants
| Level: | $120$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot6\cdot10\cdot30$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30G3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&60\\85&113\end{bmatrix}$, $\begin{bmatrix}28&39\\49&68\end{bmatrix}$, $\begin{bmatrix}59&43\\113&54\end{bmatrix}$, $\begin{bmatrix}77&90\\68&79\end{bmatrix}$, $\begin{bmatrix}104&97\\113&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.3.bt.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $368640$ |
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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $16$ | $8$ | $0$ | $0$ |
| 24.16.0-24.d.1.1 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.48.1-15.a.1.4 | $30$ | $2$ | $2$ | $1$ | $0$ |
| 120.48.1-15.a.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 24.16.0-24.d.1.1 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.192.5-120.id.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.id.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ie.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ie.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ig.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ig.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ih.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ih.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lf.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lf.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lg.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lg.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.li.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.li.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lj.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.lj.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.288.7-120.gsw.1.41 | $120$ | $3$ | $3$ | $7$ |
| 120.288.9-120.nyi.1.16 | $120$ | $3$ | $3$ | $9$ |
| 120.384.13-120.el.1.1 | $120$ | $4$ | $4$ | $13$ |
| 120.480.15-120.zb.1.1 | $120$ | $5$ | $5$ | $15$ |