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: | 16E1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}177&32\\56&133\end{bmatrix}$, $\begin{bmatrix}179&88\\11&7\end{bmatrix}$, $\begin{bmatrix}199&0\\236&201\end{bmatrix}$, $\begin{bmatrix}201&232\\51&263\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.48.1.x.1 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 |
---|---|---|---|---|---|---|
16.48.1-16.b.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
136.48.0-136.bp.1.11 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.p.1.18 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.p.1.29 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-136.bp.1.5 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.1-16.b.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | 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.dg.1.5 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dg.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dh.1.10 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dh.2.6 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.di.1.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.di.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dj.1.6 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dj.2.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |