Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| 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 | $10^{8}\cdot40^{4}$ | Cusp orbits | $4^{3}$ | ||
| 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: | 40C15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&37\\92&107\end{bmatrix}$, $\begin{bmatrix}37&47\\72&53\end{bmatrix}$, $\begin{bmatrix}47&102\\92&91\end{bmatrix}$, $\begin{bmatrix}57&79\\20&83\end{bmatrix}$, $\begin{bmatrix}79&33\\40&101\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.15.hw.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 24.48.0-24.bi.1.4 | $24$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.48.0-24.bi.1.4 | $24$ | $10$ | $10$ | $0$ | $0$ |
| 40.240.7-40.ci.1.19 | $40$ | $2$ | $2$ | $7$ | $0$ |
| 120.240.7-120.cc.1.6 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.cc.1.21 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-40.ci.1.24 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.50 | $120$ | $2$ | $2$ | $7$ | $?$ |