Invariants
| Level: | $120$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot10^{2}\cdot30^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30N5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}68&63\\65&1\end{bmatrix}$, $\begin{bmatrix}74&7\\77&69\end{bmatrix}$, $\begin{bmatrix}87&74\\46&5\end{bmatrix}$, $\begin{bmatrix}92&7\\33&16\end{bmatrix}$, $\begin{bmatrix}116&13\\95&99\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.5.id.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $192$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| $X_{\pm1}(5)$ | $5$ | $16$ | $8$ | $0$ | $0$ |
| 24.16.0-24.d.1.1 | $24$ | $12$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.96.1-15.a.1.6 | $30$ | $2$ | $2$ | $1$ | $0$ |
| 120.96.1-15.a.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.3-120.bt.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.bt.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.cu.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.cu.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.384.9-120.cnu.3.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cnu.4.2 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cnv.3.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cnv.4.2 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cnx.1.3 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cnx.2.4 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cny.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cny.2.6 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cog.1.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cog.2.2 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.coh.1.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.coh.2.2 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.coj.3.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.coj.4.6 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cok.3.9 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cok.4.10 | $120$ | $2$ | $2$ | $9$ |