Invariants
Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}8&149\\209&212\end{bmatrix}$, $\begin{bmatrix}54&157\\187&92\end{bmatrix}$, $\begin{bmatrix}132&149\\33&264\end{bmatrix}$, $\begin{bmatrix}231&208\\62&109\end{bmatrix}$, $\begin{bmatrix}243&162\\218&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.24.1.b.1 for the level structure with $-I$) |
Cyclic 272-isogeny field degree: | $36$ |
Cyclic 272-torsion field degree: | $4608$ |
Full 272-torsion field degree: | $40108032$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0-8.n.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
272.24.0-8.n.1.6 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
272.96.1-272.b.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.f.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.h.1.5 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.j.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.by.1.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.by.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bz.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.bz.2.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.ca.1.11 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.ca.2.9 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cb.1.9 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cb.2.11 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cc.1.9 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cc.2.13 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cd.1.9 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cd.2.13 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.ce.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.ce.2.5 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cf.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cf.2.5 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cg.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cj.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.ck.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cn.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |