Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24W7 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}3&254\\232&279\end{bmatrix}$, $\begin{bmatrix}121&192\\96&247\end{bmatrix}$, $\begin{bmatrix}133&118\\292&207\end{bmatrix}$, $\begin{bmatrix}173&42\\228&305\end{bmatrix}$, $\begin{bmatrix}203&264\\124&199\end{bmatrix}$, $\begin{bmatrix}265&172\\16&191\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.7.bas.2 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
Full 312-torsion field degree: | $6709248$ |
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 |
---|---|---|---|---|---|
24.144.4-24.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
312.144.3-156.t.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-156.t.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.4-24.z.2.41 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bm.1.25 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bm.1.43 | $312$ | $2$ | $2$ | $4$ | $?$ |