Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24AI7 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}127&107\\16&195\end{bmatrix}$, $\begin{bmatrix}171&7\\16&255\end{bmatrix}$, $\begin{bmatrix}179&256\\216&229\end{bmatrix}$, $\begin{bmatrix}183&190\\56&193\end{bmatrix}$, $\begin{bmatrix}233&115\\120&217\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.7.ln.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $12$ |
Cyclic 264-torsion field degree: | $960$ |
Full 264-torsion field degree: | $2534400$ |
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 |
---|---|---|---|---|---|
24.192.3-24.gh.2.12 | $24$ | $2$ | $2$ | $3$ | $0$ |
264.96.0-264.dw.1.13 | $264$ | $4$ | $4$ | $0$ | $?$ |
264.192.3-24.gh.2.17 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.lt.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.lt.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pi.1.2 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pi.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ |