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: | $\begin{bmatrix}29&124\\82&111\end{bmatrix}$, $\begin{bmatrix}47&196\\88&3\end{bmatrix}$, $\begin{bmatrix}78&103\\175&2\end{bmatrix}$, $\begin{bmatrix}89&108\\48&85\end{bmatrix}$, $\begin{bmatrix}101&14\\88&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.120.9.h.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.d.1.2 | $240$ | $5$ | $5$ | $1$ | $?$ |
| 240.120.4-40.bq.1.8 | $240$ | $2$ | $2$ | $4$ | $?$ |
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.c.2.23 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.i.1.13 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ba.1.23 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.be.1.21 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gc.1.16 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gf.1.13 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gg.1.16 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.gj.1.13 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.jy.1.5 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kb.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kc.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kf.1.11 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.le.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.lh.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.li.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ll.1.7 | $240$ | $2$ | $2$ | $17$ |