Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}\cdot20^{2}\cdot40^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40P9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}16&35\\17&44\end{bmatrix}$, $\begin{bmatrix}70&67\\53&34\end{bmatrix}$, $\begin{bmatrix}77&72\\56&83\end{bmatrix}$, $\begin{bmatrix}79&78\\58&119\end{bmatrix}$, $\begin{bmatrix}87&40\\80&17\end{bmatrix}$, $\begin{bmatrix}94&109\\3&50\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has no real points, and therefore no 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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $24$ | $24$ | $0$ | $0$ |
| 24.24.1.cv.1 | $24$ | $6$ | $6$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.1.cv.1 | $24$ | $6$ | $6$ | $1$ | $1$ |
| 40.72.3.fc.1 | $40$ | $2$ | $2$ | $3$ | $1$ |
| 60.72.3.zr.1 | $60$ | $2$ | $2$ | $3$ | $1$ |
| 120.72.5.vu.1 | $120$ | $2$ | $2$ | $5$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.17.fxh.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.mvw.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.pvz.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.pwm.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bsgp.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bsgt.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bshf.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bshj.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzwn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzwn.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzwr.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzwr.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzxd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzxd.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzxh.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.bzxh.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagj.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagj.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagn.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagz.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cagz.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cahd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cahd.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfjt.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfjt.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfjx.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfjx.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfkj.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfkj.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfkn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfkn.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cftp.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cftp.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cftt.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cftt.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfuf.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfuf.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfuj.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cfuj.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgmz.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgnd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgnp.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgnt.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cguz.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgvd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgvo.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.cgvs.1 | $120$ | $2$ | $2$ | $17$ |