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: | $\begin{bmatrix}41&246\\192&119\end{bmatrix}$, $\begin{bmatrix}152&145\\51&262\end{bmatrix}$, $\begin{bmatrix}171&22\\8&241\end{bmatrix}$, $\begin{bmatrix}248&211\\245&0\end{bmatrix}$, $\begin{bmatrix}261&194\\262&35\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.1.hm.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 |
---|---|---|---|---|---|---|
12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.24.0-6.a.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ | 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.dh.1.17 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.gg.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jw.1.19 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jx.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.yx.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.yy.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.za.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zb.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bku.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bkv.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bla.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.blb.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.blg.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.blh.1.11 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.blm.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bln.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.144.3-264.diq.1.3 | $264$ | $3$ | $3$ | $3$ | $?$ | not computed |