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: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| 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: | 8N0 |
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 |
|---|---|---|---|---|---|
| $X_{\mathrm{sp}}(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
| 312.24.0.t.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
| 312.24.0.u.2 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.96.1.a.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.b.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.e.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.f.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.m.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.n.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.u.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.v.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bj.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bk.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bl.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bm.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bn.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bo.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.br.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bs.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bt.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.bu.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.ci.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cj.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cq.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cr.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cy.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.cz.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.3.bh.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bi.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bj.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bk.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bn.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bo.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bq.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.bt.1 | $312$ | $2$ | $2$ | $3$ |
| 312.144.8.g.2 | $312$ | $3$ | $3$ | $8$ |
| 312.192.7.f.2 | $312$ | $4$ | $4$ | $7$ |