Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $3^{8}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12S1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}59&204\\117&179\end{bmatrix}$, $\begin{bmatrix}85&258\\24&91\end{bmatrix}$, $\begin{bmatrix}185&202\\51&25\end{bmatrix}$, $\begin{bmatrix}221&60\\39&59\end{bmatrix}$, $\begin{bmatrix}259&254\\255&251\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 132.72.1.p.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $6758400$ |
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 |
---|---|---|---|---|---|---|
24.72.0-6.a.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.48.0-132.q.1.7 | $264$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
264.48.0-132.q.1.11 | $264$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
264.72.0-6.a.1.3 | $264$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.288.5-132.f.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.be.1.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.dk.1.4 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.do.1.2 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.dt.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.fw.1.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.ge.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.gu.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-132.gz.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.ig.1.6 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.bbn.1.4 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.bcp.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.bsq.1.6 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.buu.1.2 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.bzc.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.288.5-264.cal.1.4 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |