Invariants
| Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $9 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20\cdot80$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80A9 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}23&166\\8&93\end{bmatrix}$, $\begin{bmatrix}36&49\\227&102\end{bmatrix}$, $\begin{bmatrix}96&85\\65&176\end{bmatrix}$, $\begin{bmatrix}118&157\\95&144\end{bmatrix}$, $\begin{bmatrix}134&195\\155&154\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.120.9.g.1 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $96$ |
| Cyclic 240-torsion field degree: | $6144$ |
| Full 240-torsion field degree: | $2359296$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.4-40.bq.1.13 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 240.48.1-240.c.1.6 | $240$ | $5$ | $5$ | $1$ | $?$ |
| 240.120.4-40.bq.1.7 | $240$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.480.17-240.b.2.23 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.g.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.z.1.22 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.bd.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gd.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ge.1.16 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gh.1.14 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gi.1.16 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.jz.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ka.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kd.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ke.1.8 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.lf.1.8 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.lg.1.8 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.lj.1.8 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.lk.1.8 | $240$ | $2$ | $2$ | $17$ |