Invariants
| Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot2$ | ||
| 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: | 16C2 |
Level structure
| $\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}89&186\\40&33\end{bmatrix}$, $\begin{bmatrix}91&126\\232&189\end{bmatrix}$, $\begin{bmatrix}97&218\\256&261\end{bmatrix}$, $\begin{bmatrix}253&262\\152&117\end{bmatrix}$, $\begin{bmatrix}269&258\\160&221\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 272.48.2.f.1 for the level structure with $-I$) |
| Cyclic 272-isogeny field degree: | $36$ |
| Cyclic 272-torsion field degree: | $4608$ |
| Full 272-torsion field degree: | $20054016$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 272.48.0-8.i.1.6 | $272$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 272.192.3-272.cc.1.1 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.cm.1.3 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dc.1.11 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.df.2.9 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dg.2.1 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dh.2.1 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.di.2.5 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dj.1.13 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dl.1.5 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dm.1.7 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dn.2.10 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.do.2.9 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dp.1.13 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dq.1.17 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dw.1.1 | $272$ | $2$ | $2$ | $3$ |
| 272.192.3-272.dx.2.3 | $272$ | $2$ | $2$ | $3$ |