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 | $4^{8}\cdot8^{2}$ | 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: | 8N0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}73&168\\152&13\end{bmatrix}$, $\begin{bmatrix}85&256\\18&163\end{bmatrix}$, $\begin{bmatrix}155&12\\146&163\end{bmatrix}$, $\begin{bmatrix}185&24\\46&155\end{bmatrix}$, $\begin{bmatrix}235&72\\38&239\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.0.i.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
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 |
---|---|---|---|---|---|
12.48.0-12.c.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
264.48.0-12.c.1.14 | $264$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.2.30 | $88$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-88.i.2.4 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.18 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.62 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.bc.2.13 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.cm.2.13 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.de.2.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.di.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fs.1.13 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ge.1.13 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.gi.1.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.gu.1.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ie.1.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.iq.1.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.iu.1.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.jg.1.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kq.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ku.2.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kx.2.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kz.2.14 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.bd.2.57 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.x.1.18 | $264$ | $4$ | $4$ | $7$ |