Invariants
| Level: | $264$ | $\SL_2$-level: | $12$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot4^{2}\cdot6\cdot12^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
| 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: | 12J0 |
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 |
|---|---|---|---|---|---|
| $X_0(12)$ | $12$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.96.1.lg.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qh.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qt.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qu.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qv.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qw.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qx.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.qy.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.ra.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rb.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.re.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rf.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rh.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rk.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rl.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.ro.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rp.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rq.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rs.4 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rt.3 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rv.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rw.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.ry.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.rz.1 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.sc.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.sd.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.sg.3 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.sh.3 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.sz.3 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.tc.3 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.td.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.1.tg.2 | $264$ | $2$ | $2$ | $1$ |
| 264.96.3.pm.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.pp.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.pq.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.pt.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.ql.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qm.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qp.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qq.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qs.3 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qv.3 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qw.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.qz.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.rb.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.rc.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.rf.3 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.rg.3 | $264$ | $2$ | $2$ | $3$ |
| 264.144.3.c.2 | $264$ | $3$ | $3$ | $3$ |