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: | $\begin{bmatrix}13&16\\82&89\end{bmatrix}$, $\begin{bmatrix}129&80\\36&95\end{bmatrix}$, $\begin{bmatrix}133&200\\126&19\end{bmatrix}$, $\begin{bmatrix}141&144\\246&71\end{bmatrix}$, $\begin{bmatrix}213&264\\72&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.96.1.r.1 for the level structure with $-I$) |
Cyclic 272-isogeny field degree: | $36$ |
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 |
---|---|---|---|---|---|---|
16.96.0-16.d.2.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.96.0-136.bd.1.3 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-16.d.2.9 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-136.bd.1.11 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bl.1.1 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bl.1.16 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.br.2.3 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.br.2.14 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.1-272.b.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.b.2.6 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bz.2.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bz.2.14 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cf.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cf.1.16 | $272$ | $2$ | $2$ | $1$ | $?$ | 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.cp.2.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.dy.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hj.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ht.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jk.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jl.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jo.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jp.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jw.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jx.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ka.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.kb.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |