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 | $2^{3}\cdot4$ | ||
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.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
312.24.0.t.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.24.0.x.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.a.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.d.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.ba.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.bf.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.ds.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.dt.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.dy.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.dz.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gi.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gj.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gk.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gl.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gy.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.gz.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.ha.1 | $312$ | $2$ | $2$ | $1$ |
312.96.1.hb.1 | $312$ | $2$ | $2$ | $1$ |
312.144.8.lu.2 | $312$ | $3$ | $3$ | $8$ |
312.192.7.go.2 | $312$ | $4$ | $4$ | $7$ |