Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16H3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}13&224\\94&21\end{bmatrix}$, $\begin{bmatrix}57&136\\46&21\end{bmatrix}$, $\begin{bmatrix}65&92\\34&83\end{bmatrix}$, $\begin{bmatrix}161&164\\218&235\end{bmatrix}$, $\begin{bmatrix}205&208\\238&161\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.ih.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $3072$ |
| Full 240-torsion field degree: | $2949120$ |
Rational points
This modular curve has no $\Q_p$ points for $p=29$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.96.1-40.bv.1.3 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 48.96.1-48.b.1.2 | $48$ | $2$ | $2$ | $1$ | $0$ |
| 240.96.1-48.b.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.2.43 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-40.bv.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.384.5-240.kq.1.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.kq.2.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.la.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.la.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ty.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ty.2.8 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ue.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ue.2.8 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bfb.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bfb.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bfe.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bfe.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bgc.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bgc.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bgd.1.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bgd.2.3 | $240$ | $2$ | $2$ | $5$ |