Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}17&28\\44&69\end{bmatrix}$, $\begin{bmatrix}79&10\\252&203\end{bmatrix}$, $\begin{bmatrix}167&136\\204&245\end{bmatrix}$, $\begin{bmatrix}201&46\\92&215\end{bmatrix}$, $\begin{bmatrix}211&118\\84&203\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.dk.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $10137600$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.48.0-24.h.1.32 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.48.1-88.c.1.12 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.0-24.h.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.t.2.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.t.2.48 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.1-88.c.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.192.1-264.f.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.z.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.dl.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.dn.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.fs.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.fw.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.gz.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.hd.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.mb.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.mf.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.nh.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.nl.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ol.1.11 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.on.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.os.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ot.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.288.9-264.rh.2.63 | $264$ | $3$ | $3$ | $9$ | $?$ | not computed |
264.384.9-264.jf.1.26 | $264$ | $4$ | $4$ | $9$ | $?$ | not computed |