Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24C9 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}11&24\\96&209\end{bmatrix}$, $\begin{bmatrix}41&14\\56&85\end{bmatrix}$, $\begin{bmatrix}127&180\\216&181\end{bmatrix}$, $\begin{bmatrix}133&4\\24&149\end{bmatrix}$, $\begin{bmatrix}145&240\\256&245\end{bmatrix}$, $\begin{bmatrix}203&10\\184&241\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.144.9.bbe.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 2 rational cusps but no known non-cuspidal 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 |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
88.96.1-88.bu.1.1 | $88$ | $3$ | $3$ | $1$ | $?$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
88.96.1-88.bu.1.1 | $88$ | $3$ | $3$ | $1$ | $?$ |
132.144.4-132.c.1.13 | $132$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-132.c.1.51 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-24.ch.1.46 | $264$ | $2$ | $2$ | $4$ | $?$ |
264.144.5-264.c.1.14 | $264$ | $2$ | $2$ | $5$ | $?$ |
264.144.5-264.c.1.78 | $264$ | $2$ | $2$ | $5$ | $?$ |