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: | $10$ (of which $2$ are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24D8 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}5&154\\208&61\end{bmatrix}$, $\begin{bmatrix}47&240\\0&197\end{bmatrix}$, $\begin{bmatrix}85&118\\88&113\end{bmatrix}$, $\begin{bmatrix}121&254\\16&181\end{bmatrix}$, $\begin{bmatrix}201&286\\256&285\end{bmatrix}$, $\begin{bmatrix}233&264\\288&157\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.8.pm.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 2 rational cusps but no known non-cuspidal 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.bk.1.74 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bk.1.82 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bn.2.20 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bn.2.76 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-24.ch.1.27 | $312$ | $2$ | $2$ | $4$ | $?$ |