Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24F2 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&98\\10&11\end{bmatrix}$, $\begin{bmatrix}42&55\\41&76\end{bmatrix}$, $\begin{bmatrix}78&31\\77&112\end{bmatrix}$, $\begin{bmatrix}80&31\\69&46\end{bmatrix}$, $\begin{bmatrix}89&58\\86&3\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.2.f.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $368640$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-12.f.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 120.48.0-12.f.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.192.3-120.eo.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.ho.1.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.ig.2.9 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.il.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.lm.2.7 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.lo.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.lq.2.9 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.ls.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.mt.1.15 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.mu.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.mx.2.15 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.my.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.nj.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.nk.2.7 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.nn.2.13 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.no.2.9 | $120$ | $2$ | $2$ | $3$ |
| 120.288.7-120.dki.1.7 | $120$ | $3$ | $3$ | $7$ |
| 120.480.18-120.i.1.2 | $120$ | $5$ | $5$ | $18$ |