Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | ||||
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 | $2^{4}\cdot8^{2}$ | 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: | $\begin{bmatrix}147&172\\112&111\end{bmatrix}$, $\begin{bmatrix}187&276\\97&185\end{bmatrix}$, $\begin{bmatrix}213&188\\244&193\end{bmatrix}$, $\begin{bmatrix}225&200\\62&53\end{bmatrix}$, $\begin{bmatrix}247&100\\165&305\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.24.0.bi.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
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 |
---|---|---|---|---|---|
12.24.0-4.d.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
104.24.0-4.d.1.6 | $104$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
312.96.1-312.lg.1.3 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.lh.1.4 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.li.1.4 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.lj.1.6 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.lk.1.2 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.ll.1.4 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.lm.1.8 | $312$ | $2$ | $2$ | $1$ |
312.96.1-312.ln.1.3 | $312$ | $2$ | $2$ | $1$ |
312.144.4-312.gb.1.16 | $312$ | $3$ | $3$ | $4$ |
312.192.3-312.jl.1.3 | $312$ | $4$ | $4$ | $3$ |