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 | $2^{5}$ | ||
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: | $\begin{bmatrix}49&136\\228&89\end{bmatrix}$, $\begin{bmatrix}125&216\\250&53\end{bmatrix}$, $\begin{bmatrix}169&56\\240&263\end{bmatrix}$, $\begin{bmatrix}173&48\\242&89\end{bmatrix}$, $\begin{bmatrix}181&200\\136&51\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.0.cw.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
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 |
---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
264.48.0-8.i.1.9 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.3 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.t.2.21 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.ec.1.10 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.ec.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.v.2.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fo.2.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kx.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.lb.2.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ot.1.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ox.1.3 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.pt.1.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.qb.1.3 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.pc.1.41 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.jo.1.37 | $264$ | $4$ | $4$ | $7$ |