Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}41&212\\12&311\end{bmatrix}$, $\begin{bmatrix}167&200\\196&249\end{bmatrix}$, $\begin{bmatrix}207&44\\224&73\end{bmatrix}$, $\begin{bmatrix}289&180\\268&143\end{bmatrix}$, $\begin{bmatrix}305&152\\292&171\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.cz.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $10063872$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.0-8.c.1.8 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.96.0-312.b.2.13 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.b.2.32 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-8.c.1.7 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-312.o.2.39 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.o.2.40 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
312.384.5-312.hf.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hf.1.11 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hg.2.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hg.2.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hi.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hi.1.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hj.2.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hj.2.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hm.2.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hm.2.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hn.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hn.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hr.2.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hr.2.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hv.3.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hv.3.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |