Invariants
Level: | $272$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/272\Z)$-generators: | $\begin{bmatrix}9&232\\36&175\end{bmatrix}$, $\begin{bmatrix}13&216\\84&167\end{bmatrix}$, $\begin{bmatrix}125&104\\270&7\end{bmatrix}$, $\begin{bmatrix}133&48\\234&257\end{bmatrix}$, $\begin{bmatrix}221&96\\224&143\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 272.96.1.i.2 for the level structure with $-I$) |
Cyclic 272-isogeny field degree: | $36$ |
Cyclic 272-torsion field degree: | $2304$ |
Full 272-torsion field degree: | $10027008$ |
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 |
---|---|---|---|---|---|---|
8.96.0-8.l.2.4 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
272.96.0-272.f.1.2 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.f.1.22 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-8.l.2.6 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bn.2.4 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bn.2.13 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bp.1.8 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.0-272.bp.1.9 | $272$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
272.96.1-272.b.2.1 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.b.2.12 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cb.1.8 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cb.1.9 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cd.2.4 | $272$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
272.96.1-272.cd.2.13 | $272$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
272.384.5-272.db.3.6 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.dc.2.4 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ea.2.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.eb.2.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hx.2.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hy.2.4 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ih.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ii.2.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.it.2.4 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.iu.2.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.jd.2.4 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.je.2.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |