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: | 24B8 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}43&108\\248&41\end{bmatrix}$, $\begin{bmatrix}117&76\\80&9\end{bmatrix}$, $\begin{bmatrix}131&88\\232&205\end{bmatrix}$, $\begin{bmatrix}175&30\\224&5\end{bmatrix}$, $\begin{bmatrix}259&244\\304&65\end{bmatrix}$, $\begin{bmatrix}265&122\\144&89\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.8.pj.2 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 $p=127$, 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 | $24$ | $2$ | $2$ | $4$ | $0$ |
312.96.0-312.cy.1.3 | $312$ | $3$ | $3$ | $0$ | $?$ |
312.144.4-312.bj.2.97 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bj.2.105 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-24.ch.1.25 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.on.1.11 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.on.1.54 | $312$ | $2$ | $2$ | $4$ | $?$ |