Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | ||||
| Index: | $24$ | $\PSL_2$-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 | $1^{4}\cdot4\cdot16$ | 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: | 16C0 |
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 |
|---|---|---|---|---|---|
| $X_0(8)$ | $8$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.48.0.cy.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cy.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cz.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cz.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.da.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.da.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.db.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.db.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dc.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dc.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dd.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dd.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.de.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.de.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.df.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.df.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dg.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dg.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dh.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dh.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.di.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.di.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dj.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dj.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dk.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dk.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dl.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dl.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dm.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dm.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dn.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dn.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.1.a.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.f.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.g.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.j.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.q.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.t.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.u.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.x.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bq.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bt.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bu.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bx.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.cg.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.cj.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ck.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.cn.1 | $240$ | $2$ | $2$ | $1$ |
| 240.72.4.cn.1 | $240$ | $3$ | $3$ | $4$ |
| 240.96.3.chs.1 | $240$ | $4$ | $4$ | $3$ |
| 240.120.8.v.1 | $240$ | $5$ | $5$ | $8$ |
| 240.144.7.yj.1 | $240$ | $6$ | $6$ | $7$ |
| 240.240.15.bx.1 | $240$ | $10$ | $10$ | $15$ |