Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}1&172\\140&231\end{bmatrix}$, $\begin{bmatrix}121&112\\180&241\end{bmatrix}$, $\begin{bmatrix}145&60\\44&239\end{bmatrix}$, $\begin{bmatrix}205&92\\108&203\end{bmatrix}$, $\begin{bmatrix}205&128\\80&209\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.1.v.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.1-8.h.1.2 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
264.96.0-264.a.1.21 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.a.1.25 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.b.1.21 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.b.1.45 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.cw.1.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.cw.1.24 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.cx.2.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.cx.2.28 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-8.h.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.m.2.11 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.m.2.22 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.q.2.22 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.q.2.25 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
264.384.5-264.dd.1.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.dd.3.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.de.1.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.de.3.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.dj.1.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.dj.3.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.dk.1.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.dk.3.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |