Invariants
| Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M5 |
Level structure
| $\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}45&8\\241&267\end{bmatrix}$, $\begin{bmatrix}185&64\\154&81\end{bmatrix}$, $\begin{bmatrix}229&120\\76&97\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 272.192.5.lo.1 for the level structure with $-I$) |
| Cyclic 272-isogeny field degree: | $36$ |
| Cyclic 272-torsion field degree: | $1152$ |
| Full 272-torsion field degree: | $5013504$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.1-16.l.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 136.192.1-136.cm.2.7 | $136$ | $2$ | $2$ | $1$ | $?$ |
| 272.192.1-16.l.1.4 | $272$ | $2$ | $2$ | $1$ | $?$ |
| 272.192.1-272.bf.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ |
| 272.192.1-272.bf.2.11 | $272$ | $2$ | $2$ | $1$ | $?$ |
| 272.192.1-136.cm.2.6 | $272$ | $2$ | $2$ | $1$ | $?$ |
| 272.192.3-272.gl.1.2 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.gl.1.5 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.gz.1.1 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.gz.1.10 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.ha.2.3 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.ha.2.5 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.hb.1.3 | $272$ | $2$ | $2$ | $3$ | $?$ |
| 272.192.3-272.hb.1.12 | $272$ | $2$ | $2$ | $3$ | $?$ |