Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12K3 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}67&204\\30&259\end{bmatrix}$, $\begin{bmatrix}105&224\\200&141\end{bmatrix}$, $\begin{bmatrix}193&148\\174&191\end{bmatrix}$, $\begin{bmatrix}207&20\\92&243\end{bmatrix}$, $\begin{bmatrix}235&90\\12&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.dm.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
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 |
---|---|---|---|---|---|
24.96.1-24.bz.1.20 | $24$ | $2$ | $2$ | $1$ | $1$ |
132.96.1-132.d.1.17 | $132$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-132.d.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-24.bz.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.384.5-264.km.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.km.2.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.km.3.11 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.km.4.11 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kp.1.8 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kp.2.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kp.3.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kp.4.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.py.1.3 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.py.2.9 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.py.3.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.py.4.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.2.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.3.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.4.16 | $264$ | $2$ | $2$ | $5$ |