Invariants
Level: | $264$ | $\SL_2$-level: | $88$ | 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 $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot11^{2}\cdot22\cdot88$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 88B9 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}46&67\\15&98\end{bmatrix}$, $\begin{bmatrix}90&133\\107&204\end{bmatrix}$, $\begin{bmatrix}144&31\\179&172\end{bmatrix}$, $\begin{bmatrix}199&144\\14&65\end{bmatrix}$, $\begin{bmatrix}223&130\\30&235\end{bmatrix}$, $\begin{bmatrix}233&242\\40&39\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.144.9.ijw.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $8$ |
Cyclic 264-torsion field degree: | $640$ |
Full 264-torsion field degree: | $3379200$ |
Rational points
This modular curve has 4 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 |
---|---|---|---|---|---|
$X_0(11)$ | $11$ | $24$ | $12$ | $1$ | $0$ |
24.24.0-24.y.1.9 | $24$ | $12$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.24.0-24.y.1.9 | $24$ | $12$ | $12$ | $0$ | $0$ |
88.144.4-44.c.1.18 | $88$ | $2$ | $2$ | $4$ | $?$ |
264.144.4-44.c.1.25 | $264$ | $2$ | $2$ | $4$ | $?$ |