Invariants
| Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16G1 |
Level structure
| $\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}41&208\\104&89\end{bmatrix}$, $\begin{bmatrix}69&26\\264&83\end{bmatrix}$, $\begin{bmatrix}80&199\\177&26\end{bmatrix}$, $\begin{bmatrix}218&65\\27&196\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 272.48.1.ca.2 for the level structure with $-I$) |
| Cyclic 272-isogeny field degree: | $36$ |
| Cyclic 272-torsion field degree: | $2304$ |
| Full 272-torsion field degree: | $20054016$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.48.0-8.ba.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 272.48.0-8.ba.1.8 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 272.48.0-272.m.2.8 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 272.48.0-272.m.2.17 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 272.48.1-272.b.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.48.1-272.b.1.17 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 272.192.1-272.g.1.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.z.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.bj.1.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.bx.1.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.do.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.dy.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.ec.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 272.192.1-272.eq.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |