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: | $\begin{bmatrix}35&192\\16&109\end{bmatrix}$, $\begin{bmatrix}53&178\\224&81\end{bmatrix}$, $\begin{bmatrix}73&90\\192&89\end{bmatrix}$, $\begin{bmatrix}117&40\\4&251\end{bmatrix}$, $\begin{bmatrix}235&142\\8&247\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.0.h.1 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 |
---|---|---|---|---|---|
24.48.0-8.d.2.9 | $24$ | $2$ | $2$ | $0$ | $0$ |
264.48.0-44.c.1.2 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-44.c.1.11 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-8.d.2.7 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-88.i.2.14 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-88.i.2.18 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.192.1-88.c.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.t.2.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.ba.2.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.be.2.1 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.bs.2.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.bw.2.6 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.ca.2.5 | $264$ | $2$ | $2$ | $1$ |
264.192.1-88.cc.2.6 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ft.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fz.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.gy.2.4 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.he.1.9 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ma.2.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mg.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ng.1.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.nm.2.11 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.bs.2.62 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.cc.1.54 | $264$ | $4$ | $4$ | $7$ |