Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}33&52\\46&43\end{bmatrix}$, $\begin{bmatrix}73&76\\28&27\end{bmatrix}$, $\begin{bmatrix}93&68\\32&91\end{bmatrix}$, $\begin{bmatrix}109&28\\68&7\end{bmatrix}$, $\begin{bmatrix}113&84\\14&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.0.cz.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $368640$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 120.48.0-8.i.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.t.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.t.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.u.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.u.2.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.