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 | $2^{4}\cdot8^{2}$ | 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: | 8G0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}79&48\\17&161\end{bmatrix}$, $\begin{bmatrix}97&104\\263&257\end{bmatrix}$, $\begin{bmatrix}127&64\\71&69\end{bmatrix}$, $\begin{bmatrix}189&64\\83&207\end{bmatrix}$, $\begin{bmatrix}241&184\\196&105\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.24.0.cx.1 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 |
|---|---|---|---|---|---|
| 8.24.0-8.n.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 264.24.0-8.n.1.3 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.96.0-264.dz.1.6 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.dz.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.dz.2.2 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.dz.2.11 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ea.1.6 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ea.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ea.2.4 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ea.2.5 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.eb.1.3 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.eb.1.10 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.eb.2.8 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.eb.2.10 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ec.1.5 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ec.1.10 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ec.2.4 | $264$ | $2$ | $2$ | $0$ |
| 264.96.0-264.ec.2.14 | $264$ | $2$ | $2$ | $0$ |
| 264.144.4-264.ld.1.10 | $264$ | $3$ | $3$ | $4$ |
| 264.192.3-264.mv.1.20 | $264$ | $4$ | $4$ | $3$ |