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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}37&102\\160&223\end{bmatrix}$, $\begin{bmatrix}127&30\\294&23\end{bmatrix}$, $\begin{bmatrix}133&126\\194&173\end{bmatrix}$, $\begin{bmatrix}163&138\\22&277\end{bmatrix}$, $\begin{bmatrix}181&246\\280&235\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.li.2 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
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 |
---|---|---|---|---|---|---|
12.96.1-12.c.1.10 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
312.96.0-312.o.1.32 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.1.58 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.16 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.34 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-12.c.1.8 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.hw.1.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hw.2.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ia.2.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ia.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ig.3.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ig.4.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.il.3.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.il.4.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ph.2.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ph.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pl.3.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pl.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.po.1.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.po.2.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ps.3.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ps.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |