Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12E5 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}69&202\\56&97\end{bmatrix}$, $\begin{bmatrix}83&12\\188&217\end{bmatrix}$, $\begin{bmatrix}111&2\\22&125\end{bmatrix}$, $\begin{bmatrix}159&28\\214&87\end{bmatrix}$, $\begin{bmatrix}163&150\\78&103\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 264.384.5-264.kw.3.1, 264.384.5-264.kw.3.2, 264.384.5-264.kw.3.3, 264.384.5-264.kw.3.4, 264.384.5-264.kw.3.5, 264.384.5-264.kw.3.6, 264.384.5-264.kw.3.7, 264.384.5-264.kw.3.8, 264.384.5-264.kw.3.9, 264.384.5-264.kw.3.10, 264.384.5-264.kw.3.11, 264.384.5-264.kw.3.12, 264.384.5-264.kw.3.13, 264.384.5-264.kw.3.14, 264.384.5-264.kw.3.15, 264.384.5-264.kw.3.16 |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $1920$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|
24.96.1.cp.2 | $24$ | $2$ | $2$ | $1$ | $1$ |
132.96.3.q.1 | $132$ | $2$ | $2$ | $3$ | $?$ |
264.96.1.lp.2 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1.lt.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.3.dp.1 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.96.3.el.2 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.96.3.er.2 | $264$ | $2$ | $2$ | $3$ | $?$ |