Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40M7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&20\\6&113\end{bmatrix}$, $\begin{bmatrix}41&0\\117&67\end{bmatrix}$, $\begin{bmatrix}47&100\\33&119\end{bmatrix}$, $\begin{bmatrix}63&20\\83&19\end{bmatrix}$, $\begin{bmatrix}89&40\\71&107\end{bmatrix}$, $\begin{bmatrix}99&20\\107&103\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.7.dko.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $4$ |
| Cyclic 120-torsion field degree: | $64$ |
| Full 120-torsion field degree: | $122880$ |
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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 24.48.0-24.bj.1.5 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.48.0-24.bj.1.5 | $24$ | $6$ | $6$ | $0$ | $0$ |
| 40.144.3-40.bx.1.12 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 120.144.3-40.bx.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.bec.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.bec.1.24 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.byp.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.byp.1.56 | $120$ | $2$ | $2$ | $3$ | $?$ |