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 $4$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot4$ | ||
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: | 16E1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}85&176\\112&213\end{bmatrix}$, $\begin{bmatrix}85&264\\44&29\end{bmatrix}$, $\begin{bmatrix}89&100\\254&227\end{bmatrix}$, $\begin{bmatrix}245&8\\150&41\end{bmatrix}$, $\begin{bmatrix}253&40\\136&265\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.48.1.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: | $20054016$ |
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.1.5 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.q.1.8 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.0-272.q.1.9 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.48.1-272.d.1.8 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.48.1-272.d.1.9 | $272$ | $2$ | $2$ | $1$ | $?$ | 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.h.1.2 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.h.2.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.q.1.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.1-272.q.2.3 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.192.3-272.cb.1.2 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.ci.1.12 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.ci.2.10 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.cl.1.19 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.cl.2.3 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.cn.1.8 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dd.1.2 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dl.1.5 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dl.2.1 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dn.1.13 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dn.2.10 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |
272.192.3-272.dr.2.6 | $272$ | $2$ | $2$ | $3$ | $?$ | not computed |