Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16H0 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}87&124\\86&29\end{bmatrix}$, $\begin{bmatrix}96&185\\203&14\end{bmatrix}$, $\begin{bmatrix}124&109\\15&98\end{bmatrix}$, $\begin{bmatrix}128&75\\203&152\end{bmatrix}$, $\begin{bmatrix}212&31\\187&184\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.48.0.de.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $1536$ |
| Full 240-torsion field degree: | $5898240$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.48.0-8.ba.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 240.48.0-8.ba.1.4 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.48.0-240.m.2.17 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.48.0-240.m.2.32 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.48.0-240.p.1.8 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.48.0-240.p.1.39 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.192.1-240.j.1.2 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.cx.2.15 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.ea.1.8 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.fp.1.7 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.jb.1.8 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.jt.2.16 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.kb.1.8 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.lf.1.8 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.ln.1.7 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.mj.1.8 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.mr.1.4 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.nr.1.4 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.nz.1.7 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.ov.1.7 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.pd.1.4 | $240$ | $2$ | $2$ | $1$ |
| 240.192.1-240.qd.1.3 | $240$ | $2$ | $2$ | $1$ |
| 240.288.8-240.ua.1.15 | $240$ | $3$ | $3$ | $8$ |
| 240.384.7-240.yv.2.13 | $240$ | $4$ | $4$ | $7$ |
| 240.480.16-240.eg.1.29 | $240$ | $5$ | $5$ | $16$ |