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: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-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: | $\begin{bmatrix}7&192\\82&253\end{bmatrix}$, $\begin{bmatrix}103&8\\150&151\end{bmatrix}$, $\begin{bmatrix}161&80\\44&103\end{bmatrix}$, $\begin{bmatrix}187&20\\136&13\end{bmatrix}$, $\begin{bmatrix}199&104\\2&129\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.ca.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $7680$ |
| Full 264-torsion field degree: | $10137600$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 264.48.0-8.e.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.2.45 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.2.58 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.y.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.y.1.31 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.bb.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.be.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.cz.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.da.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.eo.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ep.1.8 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ew.1.7 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ex.1.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.fw.1.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.fx.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ge.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gf.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.hs.2.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ht.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ia.1.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ib.1.4 | $264$ | $2$ | $2$ | $1$ |
| 264.288.8-264.mo.2.27 | $264$ | $3$ | $3$ | $8$ |
| 264.384.7-264.gv.2.40 | $264$ | $4$ | $4$ | $7$ |