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: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16H3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}61&212\\76&175\end{bmatrix}$, $\begin{bmatrix}69&160\\142&17\end{bmatrix}$, $\begin{bmatrix}97&44\\56&131\end{bmatrix}$, $\begin{bmatrix}125&236\\82&3\end{bmatrix}$, $\begin{bmatrix}157&4\\90&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.ej.1 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 |
|---|---|---|---|---|---|
| 8.96.1-8.p.1.2 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.1.27 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.2.35 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-8.p.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
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.lc.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lc.2.8 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.le.1.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.le.2.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lf.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lf.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lg.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lg.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.li.1.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.li.2.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lk.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lk.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ll.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ll.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lm.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lm.2.8 | $240$ | $2$ | $2$ | $5$ |