Invariants
Level: | $312$ | $\SL_2$-level: | $4$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4G0 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}89&66\\62&181\end{bmatrix}$, $\begin{bmatrix}213&142\\238&87\end{bmatrix}$, $\begin{bmatrix}255&118\\122&307\end{bmatrix}$, $\begin{bmatrix}309&14\\44&305\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.24.0.f.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $224$ |
Cyclic 312-torsion field degree: | $21504$ |
Full 312-torsion field degree: | $40255488$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.24.0-8.b.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
156.24.0-52.a.1.3 | $156$ | $2$ | $2$ | $0$ | $?$ |
312.24.0-52.a.1.2 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.24.0-8.b.1.4 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.24.0-104.b.1.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.24.0-104.b.1.7 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
312.144.4-312.f.1.22 | $312$ | $3$ | $3$ | $4$ |
312.192.3-312.dt.1.23 | $312$ | $4$ | $4$ | $3$ |