Invariants
| Level: | $264$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8I0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}10&211\\105&92\end{bmatrix}$, $\begin{bmatrix}20&245\\181&60\end{bmatrix}$, $\begin{bmatrix}85&164\\256&121\end{bmatrix}$, $\begin{bmatrix}170&67\\83&66\end{bmatrix}$, $\begin{bmatrix}205&138\\82&61\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.24.0.bu.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $20275200$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.0-8.n.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 264.24.0-8.n.1.2 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.96.0-88.z.2.1 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bc.1.6 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bd.2.6 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.be.1.8 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bg.1.1 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bj.2.8 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bl.2.6 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-88.bm.2.8 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.de.1.4 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.dg.1.4 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.di.2.12 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.dk.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ea.1.2 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ef.1.4 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ej.2.10 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.em.1.11 | $264$ | $2$ | $2$ | $0$ |
| 264.144.4-264.no.1.18 | $264$ | $3$ | $3$ | $4$ |
| 264.192.3-264.ph.2.29 | $264$ | $4$ | $4$ | $3$ |