Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24B8 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}1&162\\128&77\end{bmatrix}$, $\begin{bmatrix}13&10\\88&221\end{bmatrix}$, $\begin{bmatrix}41&146\\80&229\end{bmatrix}$, $\begin{bmatrix}59&158\\8&33\end{bmatrix}$, $\begin{bmatrix}167&42\\144&101\end{bmatrix}$, $\begin{bmatrix}213&58\\112&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.144.8.pm.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $3379200$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=127$, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
88.96.0-88.bb.2.3 | $88$ | $3$ | $3$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
88.96.0-88.bb.2.3 | $88$ | $3$ | $3$ | $0$ | $?$ |
264.144.4-264.bp.1.97 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-264.bp.1.101 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-24.ch.1.10 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-264.nv.2.11 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-264.nv.2.54 | $264$ | $2$ | $2$ | $4$ | $?$ |