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: | $12$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{2}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| 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: | 16N3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}62&195\\33&148\end{bmatrix}$, $\begin{bmatrix}81&8\\136&81\end{bmatrix}$, $\begin{bmatrix}108&163\\83&76\end{bmatrix}$, $\begin{bmatrix}113&26\\134&189\end{bmatrix}$, $\begin{bmatrix}164&75\\125&238\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.blg.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 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 |
|---|---|---|---|---|---|
| 48.96.1-16.v.2.2 | $48$ | $2$ | $2$ | $1$ | $0$ |
| 80.96.1-16.v.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ |
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.bny.1.8 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bpc.1.11 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.brm.2.10 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.caq.1.13 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ccd.1.16 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cco.1.12 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ccy.1.14 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cdl.1.15 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cdz.1.14 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cek.1.9 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cem.1.10 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cev.1.9 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cfj.1.15 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cfy.1.10 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cgi.1.13 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cgz.1.11 | $240$ | $2$ | $2$ | $5$ |