Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | ||||
| 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 | $1^{4}\cdot3^{4}\cdot8\cdot24$ | 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: | 24B0 |
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 |
|---|---|---|---|---|
| 168.96.1.sb.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sb.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sc.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sc.3 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sf.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sf.4 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sg.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sg.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sj.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sj.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sk.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sk.3 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sn.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sn.4 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.so.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.so.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sr.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sr.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ss.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ss.4 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sv.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sv.3 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sw.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sw.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sz.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.sz.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ta.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ta.4 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.td.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.td.3 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.te.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.te.2 | $168$ | $2$ | $2$ | $1$ |
| 168.96.3.dt.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ft.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ii.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ik.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.jp.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.jq.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.kb.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.kc.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.oj.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ok.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.on.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.oo.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.oz.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.pa.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.pd.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.pe.2 | $168$ | $2$ | $2$ | $3$ |
| 168.144.3.g.1 | $168$ | $3$ | $3$ | $3$ |
| 168.384.23.lw.1 | $168$ | $8$ | $8$ | $23$ |