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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 12P1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}27&122\\94&35\end{bmatrix}$, $\begin{bmatrix}29&258\\36&227\end{bmatrix}$, $\begin{bmatrix}35&76\\92&177\end{bmatrix}$, $\begin{bmatrix}45&56\\260&75\end{bmatrix}$, $\begin{bmatrix}133&66\\216&127\end{bmatrix}$, $\begin{bmatrix}169&92\\40&177\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.di.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 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 |
---|---|---|---|---|---|---|
12.48.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.24.0-264.a.1.9 | $264$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
264.48.0-6.a.1.12 | $264$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.192.1-264.ls.1.25 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.1.30 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.2.26 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.2.29 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.3.20 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.3.27 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.4.19 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ls.4.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.1.26 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.1.29 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.2.25 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.2.30 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.3.19 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.3.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.4.20 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lu.4.27 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.cx.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cy.1.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cy.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.db.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.db.1.33 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dd.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dd.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.de.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.de.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.df.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.df.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dn.1.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dn.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.do.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.do.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.es.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.es.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.es.2.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.es.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.eu.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.eu.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.eu.2.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.eu.2.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fn.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fn.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fn.2.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fn.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fo.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fo.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fo.2.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fo.2.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.5-264.p.1.27 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |