Invariants
Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}33&112\\48&113\end{bmatrix}$, $\begin{bmatrix}61&0\\34&117\end{bmatrix}$, $\begin{bmatrix}173&32\\110&97\end{bmatrix}$, $\begin{bmatrix}181&120\\248&7\end{bmatrix}$, $\begin{bmatrix}225&184\\40&159\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.96.1.l.1 for the level structure with $-I$) |
Cyclic 272-isogeny field degree: | $18$ |
Cyclic 272-torsion field degree: | $2304$ |
Full 272-torsion field degree: | $10027008$ |
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 |
---|---|---|---|---|---|---|
16.96.1-16.b.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
136.96.0-136.bd.1.3 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.f.1.2 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.f.1.18 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-136.bd.1.12 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.cb.2.15 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.cb.2.18 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.cd.2.5 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.cd.2.12 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.1-16.b.1.12 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bl.2.13 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bl.2.20 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bn.2.7 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bn.2.10 | $272$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
272.384.5-272.co.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.dl.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.dz.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ed.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ia.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ib.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.id.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ie.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.in.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.io.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ip.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.iq.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.iw.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ix.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.iz.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ja.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |