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: | $8$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}65&24\\46&55\end{bmatrix}$, $\begin{bmatrix}109&168\\188&37\end{bmatrix}$, $\begin{bmatrix}181&224\\34&125\end{bmatrix}$, $\begin{bmatrix}189&136\\32&129\end{bmatrix}$, $\begin{bmatrix}229&232\\158&23\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.48.1.b.2 for the level structure with $-I$) |
Cyclic 272-isogeny field degree: | $36$ |
Cyclic 272-torsion field degree: | $4608$ |
Full 272-torsion field degree: | $20054016$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
272.48.0-8.i.1.2 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.o.1.16 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.o.1.17 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.1-272.b.1.16 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.48.1-272.b.1.17 | $272$ | $2$ | $2$ | $1$ | $?$ | 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.g.1.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.g.2.8 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.i.1.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.i.2.8 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.p.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.p.2.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.r.1.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.r.2.11 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.3-272.cb.2.2 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.ck.1.14 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.ck.2.10 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.cn.1.8 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dd.2.2 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dm.1.7 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dm.2.5 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dr.1.4 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |