Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}1&124\\72&35\end{bmatrix}$, $\begin{bmatrix}81&52\\164&111\end{bmatrix}$, $\begin{bmatrix}87&40\\190&97\end{bmatrix}$, $\begin{bmatrix}93&128\\242&201\end{bmatrix}$, $\begin{bmatrix}259&88\\122&249\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.0.cn.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $10137600$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-24.l.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
264.48.0-24.l.1.7 | $264$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.1.5 | $88$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-88.i.1.6 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.7 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.12 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.192.1-264.w.2.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.bh.2.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ci.1.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.cp.1.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.de.1.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.df.1.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.di.2.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.dj.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ma.1.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mb.1.9 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mm.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mn.1.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mq.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mr.2.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.nc.1.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.nd.1.1 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.oe.1.18 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.iv.1.5 | $264$ | $4$ | $4$ | $7$ |