Invariants
Level: | $264$ | $\SL_2$-level: | $4$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4G0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}11&260\\182&183\end{bmatrix}$, $\begin{bmatrix}25&164\\102&155\end{bmatrix}$, $\begin{bmatrix}145&90\\128&211\end{bmatrix}$, $\begin{bmatrix}169&148\\132&139\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.0.n.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $192$ |
Cyclic 264-torsion field degree: | $15360$ |
Full 264-torsion field degree: | $20275200$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.24.0-12.b.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
88.24.0-88.a.1.3 | $88$ | $2$ | $2$ | $0$ | $?$ |
132.24.0-12.b.1.3 | $132$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-88.a.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.b.1.2 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.b.1.13 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.144.4-264.u.1.5 | $264$ | $3$ | $3$ | $4$ |
264.192.3-264.dk.1.13 | $264$ | $4$ | $4$ | $3$ |