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 | $6^{8}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J7 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}9&212\\200&133\end{bmatrix}$, $\begin{bmatrix}131&236\\104&49\end{bmatrix}$, $\begin{bmatrix}189&124\\304&209\end{bmatrix}$, $\begin{bmatrix}199&20\\176&197\end{bmatrix}$, $\begin{bmatrix}297&196\\272&285\end{bmatrix}$, $\begin{bmatrix}309&170\\16&9\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.7.bjg.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 real points and no $\Q_p$ points for $p=5,61$, 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 | $24$ | $2$ | $2$ | $4$ | $0$ |
312.144.3-312.bh.1.39 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.bh.1.41 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.byt.1.19 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.byt.1.39 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.caw.1.10 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.caw.1.23 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.4-312.bd.1.18 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.bd.1.77 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-24.ch.1.13 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.rh.1.18 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.rh.1.40 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.sy.1.9 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.sy.1.24 | $312$ | $2$ | $2$ | $4$ | $?$ |