Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | 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: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}7&168\\54&89\end{bmatrix}$, $\begin{bmatrix}13&6\\122&263\end{bmatrix}$, $\begin{bmatrix}31&78\\142&239\end{bmatrix}$, $\begin{bmatrix}85&174\\192&49\end{bmatrix}$, $\begin{bmatrix}109&48\\222&139\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.1.ln.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.0-24.o.1.31 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.96.1-132.a.1.17 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.0-24.o.1.29 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.o.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.o.1.50 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-132.a.1.16 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.384.5-264.io.2.20 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ir.2.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.iy.1.22 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jc.2.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jw.4.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ka.3.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.kk.1.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ko.3.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.nz.1.18 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.od.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oj.1.20 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oo.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ph.3.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pm.4.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pv.3.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qa.4.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |