Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $5 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $12^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24B5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}2&35\\113&94\end{bmatrix}$, $\begin{bmatrix}5&62\\22&107\end{bmatrix}$, $\begin{bmatrix}26&115\\43&58\end{bmatrix}$, $\begin{bmatrix}27&26\\38&87\end{bmatrix}$, $\begin{bmatrix}107&24\\48&7\end{bmatrix}$, $\begin{bmatrix}112&83\\43&28\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $491520$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.36.1.fo.1 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 60.36.1.ft.1 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.24.1.lp.1 | $120$ | $3$ | $3$ | $1$ | $?$ |
| 120.36.3.o.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.144.9.bbt.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.brd.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.ciw.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.cjn.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.pkf.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.pkj.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.pku.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.pky.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vgx.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vhb.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vhn.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vhr.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vqt.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vqx.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vrj.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.vrn.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.xud.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.xuh.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.xut.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.xux.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.yff.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.yfj.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.yfv.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.yfz.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.baqp.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.baqt.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.barf.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.barj.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bbal.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bbap.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bbbb.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bbbf.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdfr.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdfv.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdgh.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdgl.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdpn.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdpr.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdqd.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bdqh.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bedf.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bedj.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bedu.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bedy.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bfhz.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bfid.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bfio.1 | $120$ | $2$ | $2$ | $9$ |
| 120.144.9.bfis.1 | $120$ | $2$ | $2$ | $9$ |