Invariants
| Level: | $312$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0.e.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 312.24.0.t.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
| 312.24.0.y.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.96.1.bb.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.be.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cz.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.da.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.eo.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ep.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ew.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ex.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.fw.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.fx.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ge.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.gf.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.hs.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ht.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ia.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ib.1 | $312$ | $2$ | $2$ | $1$ |
| 312.144.8.mv.2 | $312$ | $3$ | $3$ | $8$ |
| 312.192.7.hb.2 | $312$ | $4$ | $4$ | $7$ |