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: | $\begin{bmatrix}31&47\\69&74\end{bmatrix}$, $\begin{bmatrix}85&66\\109&77\end{bmatrix}$, $\begin{bmatrix}107&4\\14&27\end{bmatrix}$, $\begin{bmatrix}109&48\\16&101\end{bmatrix}$, $\begin{bmatrix}119&108\\107&55\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.3.c.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.a.1.2 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 60.48.1-15.a.1.11 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.48.1-15.a.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 24.16.0-24.a.1.2 | $24$ | $6$ | $6$ | $0$ | $0$ |
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.ej.1.9 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ej.2.9 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ek.1.2 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ek.2.3 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.em.1.3 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.em.2.5 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.en.1.9 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.en.2.9 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ev.1.7 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ev.2.7 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ew.1.6 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ew.2.7 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ey.1.6 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ey.2.7 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ez.1.11 | $120$ | $2$ | $2$ | $5$ |
| 120.192.5-120.ez.2.11 | $120$ | $2$ | $2$ | $5$ |
| 120.288.7-120.brf.1.25 | $120$ | $3$ | $3$ | $7$ |
| 120.288.9-120.ipd.1.7 | $120$ | $3$ | $3$ | $9$ |
| 120.384.13-120.ce.1.27 | $120$ | $4$ | $4$ | $13$ |
| 120.480.15-120.vx.1.10 | $120$ | $5$ | $5$ | $15$ |