Invariants
| Level: | $312$ | $\SL_2$-level: | $8$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 8C0 |
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 |
|---|---|---|---|---|---|
| $X_0(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.24.0.y.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.ba.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.bi.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.bj.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.by.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cb.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cd.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.ce.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cr.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cs.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cu.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.cx.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.dh.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.di.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.dw.1 | $312$ | $2$ | $2$ | $0$ |
| 312.24.0.dz.1 | $312$ | $2$ | $2$ | $0$ |
| 312.36.2.cx.1 | $312$ | $3$ | $3$ | $2$ |
| 312.48.1.zx.1 | $312$ | $4$ | $4$ | $1$ |
| 312.168.11.cl.1 | $312$ | $14$ | $14$ | $11$ |