Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}29&12\\32&233\end{bmatrix}$, $\begin{bmatrix}31&252\\56&149\end{bmatrix}$, $\begin{bmatrix}247&92\\214&219\end{bmatrix}$, $\begin{bmatrix}275&148\\270&73\end{bmatrix}$, $\begin{bmatrix}301&108\\44&89\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 312.192.1-312.pi.1.1, 312.192.1-312.pi.1.2, 312.192.1-312.pi.1.3, 312.192.1-312.pi.1.4, 312.192.1-312.pi.1.5, 312.192.1-312.pi.1.6, 312.192.1-312.pi.1.7, 312.192.1-312.pi.1.8, 312.192.1-312.pi.1.9, 312.192.1-312.pi.1.10, 312.192.1-312.pi.1.11, 312.192.1-312.pi.1.12, 312.192.1-312.pi.1.13, 312.192.1-312.pi.1.14, 312.192.1-312.pi.1.15, 312.192.1-312.pi.1.16 |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
Full 312-torsion field degree: | $20127744$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0.h.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.48.0.bb.2 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0.bg.2 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0.cx.1 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.1.ec.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.48.1.eh.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.48.1.fo.1 | $312$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.288.17.jfc.2 | $312$ | $3$ | $3$ | $17$ | $?$ | not computed |
312.384.17.dtm.2 | $312$ | $4$ | $4$ | $17$ | $?$ | not computed |