Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24Z5 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}49&276\\249&179\end{bmatrix}$, $\begin{bmatrix}187&240\\291&121\end{bmatrix}$, $\begin{bmatrix}223&192\\293&151\end{bmatrix}$, $\begin{bmatrix}301&192\\297&143\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.192.5.biv.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $2688$ |
Full 312-torsion field degree: | $5031936$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=23$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.192.3-24.gm.3.8 | $24$ | $2$ | $2$ | $3$ | $0$ |
312.192.1-312.sb.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.1-312.sb.1.22 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.1-312.sf.2.18 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.1-312.sf.2.29 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.1-312.ss.3.2 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.1-312.ss.3.25 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.192.3-24.gm.3.4 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.po.1.11 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.po.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.rt.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.rt.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.tn.1.2 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.tn.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ |