Invariants
| Level: | $264$ | $\SL_2$-level: | $8$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 8C0 |
Level structure
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 |
|---|---|---|---|---|---|
| $X_0(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.24.0.y.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.ba.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.bg.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.bh.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.bu.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.bx.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.bz.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.ca.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.cl.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.cm.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.co.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.cr.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.db.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.dc.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.dq.1 | $264$ | $2$ | $2$ | $0$ |
| 264.24.0.dt.1 | $264$ | $2$ | $2$ | $0$ |
| 264.36.2.cx.1 | $264$ | $3$ | $3$ | $2$ |
| 264.48.1.zv.1 | $264$ | $4$ | $4$ | $1$ |
| 264.144.9.ijz.1 | $264$ | $12$ | $12$ | $9$ |