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: | $\begin{bmatrix}43&14\\36&65\end{bmatrix}$, $\begin{bmatrix}56&127\\59&260\end{bmatrix}$, $\begin{bmatrix}132&87\\247&116\end{bmatrix}$, $\begin{bmatrix}161&114\\76&83\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.48.1.cf.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 |
---|---|---|---|---|---|---|
16.48.0-16.f.2.9 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.48.0-136.cb.1.8 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-16.f.2.5 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-136.cb.1.11 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.1-272.b.1.22 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.48.1-272.b.1.26 | $272$ | $2$ | $2$ | $1$ | $?$ | 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.r.2.12 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.bb.1.6 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.bq.2.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.ca.2.5 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.dp.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.ea.2.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.ee.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.er.2.6 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |