Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24D8 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}69&68\\80&93\end{bmatrix}$, $\begin{bmatrix}173&68\\80&181\end{bmatrix}$, $\begin{bmatrix}197&120\\216&29\end{bmatrix}$, $\begin{bmatrix}203&80\\140&133\end{bmatrix}$, $\begin{bmatrix}263&304\\148&85\end{bmatrix}$, $\begin{bmatrix}281&162\\96&221\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.8.pl.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $6709248$ |
Rational points
This modular curve has no $\Q_p$ points for $p=47$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
312.144.4-312.bl.2.76 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bl.2.90 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-24.ch.1.44 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.op.2.12 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.op.2.53 | $312$ | $2$ | $2$ | $4$ | $?$ |