Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $20^{2}\cdot40^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $4$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B8 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}6&47\\101&106\end{bmatrix}$, $\begin{bmatrix}31&88\\84&13\end{bmatrix}$, $\begin{bmatrix}47&90\\34&101\end{bmatrix}$, $\begin{bmatrix}73&66\\106&95\end{bmatrix}$, $\begin{bmatrix}103&44\\32&113\end{bmatrix}$ |
| 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: | $294912$ |
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 |
|---|---|---|---|---|---|
| 40.60.4.db.1 | $40$ | $2$ | $2$ | $4$ | $3$ |
| 60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
| 120.24.0.of.1 | $120$ | $5$ | $5$ | $0$ | $?$ |
| 120.60.4.go.1 | $120$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.240.17.s.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.mv.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.rq.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.st.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fpd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fpf.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fqg.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fqm.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jpi.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jpo.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jqb.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jqd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jru.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jsa.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.juz.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jvb.1 | $120$ | $2$ | $2$ | $17$ |
| 120.360.22.bvh.1 | $120$ | $3$ | $3$ | $22$ |
| 240.240.17.bep.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bet.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bhb.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bhf.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bkd.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bkh.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bmp.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.17.bmt.1 | $240$ | $2$ | $2$ | $17$ |
| 240.240.19.el.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.ep.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.nz.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.od.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.sj.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.sn.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.xh.1 | $240$ | $2$ | $2$ | $19$ |
| 240.240.19.xl.1 | $240$ | $2$ | $2$ | $19$ |
