Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}13&236\\118&117\end{bmatrix}$, $\begin{bmatrix}24&163\\167&160\end{bmatrix}$, $\begin{bmatrix}92&237\\45&38\end{bmatrix}$, $\begin{bmatrix}111&178\\94&39\end{bmatrix}$, $\begin{bmatrix}153&2\\32&183\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.1.hl.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $20275200$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.24.0-6.a.1.10 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
66.24.0-6.a.1.4 | $66$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
264.96.1-264.di.1.39 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.gh.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.kc.1.17 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.kd.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zg.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zh.1.12 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zp.1.17 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zq.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.baa.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bab.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.baj.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bak.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bam.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.ban.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bav.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.baw.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.144.3-264.cwa.1.8 | $264$ | $3$ | $3$ | $3$ | $?$ | not computed |