Invariants
Level: | $312$ | $\SL_2$-level: | $12$ | 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 | $12^{12}$ | Cusp orbits | $4^{3}$ | ||
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: | 12B7 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}55&18\\138&235\end{bmatrix}$, $\begin{bmatrix}155&60\\272&283\end{bmatrix}$, $\begin{bmatrix}265&16\\40&227\end{bmatrix}$, $\begin{bmatrix}269&292\\202&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.7.kv.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $224$ |
Cyclic 312-torsion field degree: | $21504$ |
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 |
---|---|---|---|---|---|
24.144.3-24.ba.1.5 | $24$ | $2$ | $2$ | $3$ | $1$ |
156.144.4-156.bb.1.6 | $156$ | $2$ | $2$ | $4$ | $?$ |
312.144.3-24.ba.1.7 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.dk.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.dk.1.8 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.dl.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.3-312.dl.1.16 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.144.4-312.k.1.7 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.k.1.16 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-156.bb.1.14 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.by.1.20 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.by.1.23 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.dn.1.25 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.dn.1.32 | $312$ | $2$ | $2$ | $4$ | $?$ |