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 | $1^{2}\cdot2^{3}\cdot16$ | 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: | 16D0 |
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.f.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.g.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.l.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.n.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bb.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bc.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.be.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bh.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bj.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bk.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bm.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bp.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bv.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.bw.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ca.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ch.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.co.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cp.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.de.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.df.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dq.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dr.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dy.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dz.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.eg.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.eh.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.eo.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ep.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.eu.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ev.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ey.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ez.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.1.bg.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bh.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bk.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.bl.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.cy.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.cz.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.dg.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.dh.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.eu.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ev.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.fc.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.fd.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.fo.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.fp.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ge.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.gf.1 | $240$ | $2$ | $2$ | $1$ |
| 240.72.4.cf.2 | $240$ | $3$ | $3$ | $4$ |
| 240.96.3.chn.1 | $240$ | $4$ | $4$ | $3$ |
| 240.120.8.r.2 | $240$ | $5$ | $5$ | $8$ |
| 240.144.7.uj.1 | $240$ | $6$ | $6$ | $7$ |
| 240.240.15.bp.2 | $240$ | $10$ | $10$ | $15$ |