Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot20^{6}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20K7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&50\\34&31\end{bmatrix}$, $\begin{bmatrix}5&54\\74&91\end{bmatrix}$, $\begin{bmatrix}66&13\\89&70\end{bmatrix}$, $\begin{bmatrix}78&113\\7&78\end{bmatrix}$, $\begin{bmatrix}82&85\\67&26\end{bmatrix}$, $\begin{bmatrix}104&97\\75&88\end{bmatrix}$ |
| 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 $\Q_p$ points for $p=43$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.72.3.r.1 | $40$ | $2$ | $2$ | $3$ | $1$ |
| 60.72.3.zt.1 | $60$ | $2$ | $2$ | $3$ | $1$ |
| 120.24.0.bd.1 | $120$ | $6$ | $6$ | $0$ | $?$ |
| 120.72.3.fyz.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 |
|---|---|---|---|---|
| 120.288.13.btp.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.btp.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.btv.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.btv.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bun.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bun.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.buz.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.buz.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bvt.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bvt.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwf.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwf.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwr.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwr.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwx.1 | $120$ | $2$ | $2$ | $13$ |
| 120.288.13.bwx.2 | $120$ | $2$ | $2$ | $13$ |
| 120.288.17.mga.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.mgg.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.mwa.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.mwo.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ncu.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.nde.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.nds.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.neo.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.obq.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.obq.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.obu.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.obu.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ock.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ock.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ocw.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ocw.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oeo.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oeo.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofa.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofa.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofq.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofq.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofu.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ofu.2 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oge.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oha.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ohc.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ohm.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.ohs.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oig.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oio.1 | $120$ | $2$ | $2$ | $17$ |
| 120.288.17.oiu.1 | $120$ | $2$ | $2$ | $17$ |