Invariants
| Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{6}\cdot16^{2}$ | Cusp orbits | $2^{3}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16K2 |
Level structure
| $\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}13&16\\212&55\end{bmatrix}$, $\begin{bmatrix}145&216\\208&151\end{bmatrix}$, $\begin{bmatrix}173&192\\8&37\end{bmatrix}$, $\begin{bmatrix}209&24\\198&9\end{bmatrix}$, $\begin{bmatrix}257&144\\60&103\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 272.96.2.t.1 for the level structure with $-I$) |
| Cyclic 272-isogeny field degree: | $36$ |
| Cyclic 272-torsion field degree: | $4608$ |
| Full 272-torsion field degree: | $10027008$ |
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 |
|---|---|---|---|---|---|
| 136.96.0-136.bd.1.3 | $136$ | $2$ | $2$ | $0$ | $?$ |
| 272.96.0-136.bd.1.8 | $272$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 272.384.5-272.cn.3.1 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.dr.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.ex.1.2 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.ey.1.2 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.gm.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.go.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.gy.1.1 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.ha.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.im.1.4 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.iq.1.1 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.iv.1.4 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.ix.1.2 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.jn.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.jp.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.jz.1.3 | $272$ | $2$ | $2$ | $5$ |
| 272.384.5-272.kb.1.1 | $272$ | $2$ | $2$ | $5$ |
| 272.384.7-272.bl.2.2 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.bn.2.3 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.da.2.1 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.dc.2.6 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.en.2.1 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.er.2.3 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.ez.2.3 | $272$ | $2$ | $2$ | $7$ |
| 272.384.7-272.fa.2.1 | $272$ | $2$ | $2$ | $7$ |