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: | $\begin{bmatrix}36&11\\67&76\end{bmatrix}$, $\begin{bmatrix}55&12\\122&77\end{bmatrix}$, $\begin{bmatrix}117&40\\52&49\end{bmatrix}$, $\begin{bmatrix}141&136\\52&233\end{bmatrix}$, $\begin{bmatrix}238&85\\3&164\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.3.nl.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 | $48$ | $2$ | $2$ | $1$ | $0$ |
| 240.96.1-16.v.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.384.5-80.jk.1.10 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.kr.1.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.ls.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.nr.1.2 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.oe.1.5 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.on.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.pb.1.5 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-80.pe.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cca.2.16 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ccm.1.16 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ccy.1.14 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cdk.1.14 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cfe.2.15 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cfv.1.15 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.cgn.1.13 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.chc.1.13 | $240$ | $2$ | $2$ | $5$ |