Invariants
Level: | $312$ | $\SL_2$-level: | $12$ | 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 | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | 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: | 12V1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}37&6\\142&41\end{bmatrix}$, $\begin{bmatrix}109&300\\188&199\end{bmatrix}$, $\begin{bmatrix}155&120\\276&187\end{bmatrix}$, $\begin{bmatrix}167&144\\48&235\end{bmatrix}$, $\begin{bmatrix}301&186\\164&193\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.lp.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $2688$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.96.0-12.a.2.7 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.55 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.57 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-312.dh.1.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dh.1.26 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.is.2.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.iw.3.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ix.3.24 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.jc.3.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kc.4.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ki.4.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kq.2.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kw.3.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.og.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.oh.2.24 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ol.4.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.on.4.20 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pr.1.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ps.1.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qf.2.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qg.1.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |