Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | 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 | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | 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: | 12P1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}39&1\\4&93\end{bmatrix}$, $\begin{bmatrix}51&29\\52&89\end{bmatrix}$, $\begin{bmatrix}61&86\\0&125\end{bmatrix}$, $\begin{bmatrix}85&2\\180&113\end{bmatrix}$, $\begin{bmatrix}85&119\\156&131\end{bmatrix}$, $\begin{bmatrix}179&25\\122&189\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.cad.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
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 |
---|---|---|---|---|---|---|
12.48.1-12.l.1.10 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
264.48.0-264.fl.1.10 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.fl.1.21 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.fn.1.12 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.fn.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.1-12.l.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.192.3-264.vk.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.vl.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.vo.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.vp.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ws.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wt.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wu.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wv.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ww.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wx.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wy.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.wz.1.18 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.xc.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.xd.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.xg.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.xh.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.5-264.cp.1.30 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.cr.1.28 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.jk.1.32 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.jn.1.32 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.po.1.32 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.pr.1.32 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.qv.1.30 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.192.5-264.qx.1.28 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.cai.1.1 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |