Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}31&18\\190&25\end{bmatrix}$, $\begin{bmatrix}85&228\\6&169\end{bmatrix}$, $\begin{bmatrix}97&180\\232&221\end{bmatrix}$, $\begin{bmatrix}109&54\\76&47\end{bmatrix}$, $\begin{bmatrix}163&168\\110&31\end{bmatrix}$, $\begin{bmatrix}253&210\\128&35\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.1.le.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|---|
12.96.1-12.a.1.12 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
264.96.0-264.o.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.o.1.51 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-264.o.1.58 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-12.a.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.384.5-264.a.2.20 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.c.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.d.2.40 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.g.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hw.2.14 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hz.2.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ib.2.24 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ie.2.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ln.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.lu.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.md.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.mk.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.nz.1.18 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oc.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oe.1.20 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oh.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oq.2.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ot.2.15 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ov.2.24 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oy.2.15 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qj.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qm.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qr.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qu.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.9-264.w.2.10 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.bc.2.11 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.eo.1.21 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.eu.1.23 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.la.2.10 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.lh.2.11 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.mc.1.21 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
264.384.9-264.mj.1.23 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |