Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20H3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&110\\68&69\end{bmatrix}$, $\begin{bmatrix}39&110\\62&73\end{bmatrix}$, $\begin{bmatrix}41&80\\23&81\end{bmatrix}$, $\begin{bmatrix}83&80\\8&111\end{bmatrix}$, $\begin{bmatrix}97&40\\106&57\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.cgh.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 120.72.1-20.b.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.5-120.dh.1.15 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.fs.1.7 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.nm.2.2 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.np.2.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bca.1.3 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bcb.1.7 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bcv.2.2 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bcw.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.blw.2.3 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bly.2.8 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bmr.2.2 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bms.2.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boa.2.3 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bob.2.8 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bov.2.2 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bow.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.432.15-120.lr.2.12 | $120$ | $3$ | $3$ | $15$ |