Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $8^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16A3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}24&209\\125&8\end{bmatrix}$, $\begin{bmatrix}125&108\\132&193\end{bmatrix}$, $\begin{bmatrix}125&128\\88&5\end{bmatrix}$, $\begin{bmatrix}133&222\\158&229\end{bmatrix}$, $\begin{bmatrix}161&188\\44&45\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.48.3.bl.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $96$ |
| Cyclic 240-torsion field degree: | $6144$ |
| Full 240-torsion field degree: | $5898240$ |
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 |
|---|---|---|---|---|---|
| 8.48.1-8.n.1.4 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 240.48.1-8.n.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.192.5-240.lc.2.1 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.ld.1.17 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.qv.2.6 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.qx.1.8 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.rl.2.2 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.rn.1.6 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.rz.2.6 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.sd.1.8 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.sx.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.tb.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.tv.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.tx.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.uj.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.ul.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.uv.2.5 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.uw.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.288.11-240.fu.2.6 | $240$ | $3$ | $3$ | $11$ |
| 240.384.13-240.ec.1.10 | $240$ | $4$ | $4$ | $13$ |
| 240.480.19-240.co.1.8 | $240$ | $5$ | $5$ | $19$ |