Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&58\\40&89\end{bmatrix}$, $\begin{bmatrix}7&102\\116&83\end{bmatrix}$, $\begin{bmatrix}19&35\\44&107\end{bmatrix}$, $\begin{bmatrix}39&83\\44&31\end{bmatrix}$, $\begin{bmatrix}63&115\\92&57\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.lx.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $48$ | $24$ | $0$ | $0$ |
| 40.48.0-40.bx.1.5 | $40$ | $3$ | $3$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.72.2-24.cx.1.9 | $24$ | $2$ | $2$ | $2$ | $1$ |
| 40.48.0-40.bx.1.5 | $40$ | $3$ | $3$ | $0$ | $0$ |
| 120.72.2-60.t.1.7 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-60.t.1.11 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-24.cx.1.14 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dj.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dj.1.39 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.7-120.eci.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eck.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ecy.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eda.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.enw.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eny.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eom.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eoo.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ezg.1.3 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ezi.1.10 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ezw.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ezy.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fka.1.10 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fkc.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fkq.1.2 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fks.1.5 | $120$ | $2$ | $2$ | $7$ |