Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-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 | $2^{4}\cdot8^{2}$ | 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: | 8G0 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}63&68\\113&21\end{bmatrix}$, $\begin{bmatrix}107&208\\246&175\end{bmatrix}$, $\begin{bmatrix}217&140\\51&299\end{bmatrix}$, $\begin{bmatrix}221&304\\301&163\end{bmatrix}$, $\begin{bmatrix}255&140\\272&247\end{bmatrix}$, $\begin{bmatrix}287&116\\63&173\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 312.48.0-312.bi.1.1, 312.48.0-312.bi.1.2, 312.48.0-312.bi.1.3, 312.48.0-312.bi.1.4, 312.48.0-312.bi.1.5, 312.48.0-312.bi.1.6, 312.48.0-312.bi.1.7, 312.48.0-312.bi.1.8, 312.48.0-312.bi.1.9, 312.48.0-312.bi.1.10, 312.48.0-312.bi.1.11, 312.48.0-312.bi.1.12, 312.48.0-312.bi.1.13, 312.48.0-312.bi.1.14, 312.48.0-312.bi.1.15, 312.48.0-312.bi.1.16 |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
Full 312-torsion field degree: | $80510976$ |
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 |
---|---|---|---|---|---|
4.12.0.d.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
312.12.0.z.1 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.12.0.el.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 |
---|---|---|---|---|
312.48.1.lg.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.lh.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.li.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.lj.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.lk.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.ll.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.lm.1 | $312$ | $2$ | $2$ | $1$ |
312.48.1.ln.1 | $312$ | $2$ | $2$ | $1$ |
312.72.4.gb.1 | $312$ | $3$ | $3$ | $4$ |
312.96.3.jl.1 | $312$ | $4$ | $4$ | $3$ |
312.336.23.eh.1 | $312$ | $14$ | $14$ | $23$ |