Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $3 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (of which $2$ are rational) | Cusp widths | $2^{8}\cdot4^{2}\cdot10^{8}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2^{5}\cdot4^{2}$ | ||
| 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: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20R3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&100\\52&61\end{bmatrix}$, $\begin{bmatrix}21&110\\44&1\end{bmatrix}$, $\begin{bmatrix}31&0\\52&91\end{bmatrix}$, $\begin{bmatrix}59&90\\70&101\end{bmatrix}$, $\begin{bmatrix}73&60\\18&1\end{bmatrix}$, $\begin{bmatrix}79&100\\22&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.3.b.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $128$ |
| Full 120-torsion field degree: | $122880$ |
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 |
|---|---|---|---|---|---|
| $X_1(5)$ | $5$ | $12$ | $12$ | $0$ | $0$ |
| 24.12.0-2.a.1.1 | $24$ | $24$ | $24$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_1(2,10)$ | $10$ | $2$ | $2$ | $1$ | $0$ |
| 120.144.1-10.a.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ |