Invariants
| Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $5^{4}\cdot20\cdot80$ | Cusp orbits | $1^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80B8 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}10&229\\199&48\end{bmatrix}$, $\begin{bmatrix}64&129\\189&56\end{bmatrix}$, $\begin{bmatrix}81&94\\128&19\end{bmatrix}$, $\begin{bmatrix}82&23\\181&108\end{bmatrix}$, $\begin{bmatrix}177&74\\20&99\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.120.8.w.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 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 240.48.0-240.q.1.29 | $240$ | $5$ | $5$ | $0$ | $?$ |
| 240.120.4-40.bq.1.1 | $240$ | $2$ | $2$ | $4$ | $?$ |
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.g.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ba.1.23 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.bd.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.cf.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.cg.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.cj.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ck.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dn.1.13 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.do.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dr.1.10 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ds.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ed.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ee.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.eh.1.15 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.ei.1.16 | $240$ | $2$ | $2$ | $17$ |