Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $20^{8}\cdot40^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A16 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}27&62\\44&5\end{bmatrix}$, $\begin{bmatrix}59&92\\92&15\end{bmatrix}$, $\begin{bmatrix}81&88\\104&9\end{bmatrix}$, $\begin{bmatrix}91&80\\24&89\end{bmatrix}$, $\begin{bmatrix}93&100\\100&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.16.bb.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
| 24.96.0-24.n.2.16 | $24$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.0-24.n.2.16 | $24$ | $5$ | $5$ | $0$ | $0$ |
| 40.240.8-40.n.2.12 | $40$ | $2$ | $2$ | $8$ | $0$ |
| 120.240.8-120.e.1.31 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.e.1.39 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-40.n.2.9 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.bd.1.19 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.bd.1.38 | $120$ | $2$ | $2$ | $8$ | $?$ |