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 | $2^{8}$ | ||
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: | $\begin{bmatrix}1&204\\44&289\end{bmatrix}$, $\begin{bmatrix}43&48\\16&25\end{bmatrix}$, $\begin{bmatrix}151&156\\102&19\end{bmatrix}$, $\begin{bmatrix}169&288\\40&155\end{bmatrix}$, $\begin{bmatrix}229&60\\176&301\end{bmatrix}$, $\begin{bmatrix}271&288\\12&11\end{bmatrix}$, $\begin{bmatrix}295&12\\212&137\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.lg.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
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 |
---|---|---|---|---|---|---|
12.96.1-12.b.1.12 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
312.96.0-312.o.1.21 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.1.32 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.ds.1.14 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.ds.1.49 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-12.b.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.d.1.27 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.h.2.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ig.4.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ik.4.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.lv.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.mc.1.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ml.2.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ms.1.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.mx.4.11 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.my.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.mz.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.na.2.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nf.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ng.4.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nh.2.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ni.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nn.2.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.no.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.np.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nq.4.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nv.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nw.2.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.nx.4.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ny.1.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.oj.2.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.on.2.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pa.4.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pe.4.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qn.2.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qq.1.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qv.1.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qy.1.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.9-312.bw.2.46 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.cz.3.38 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.fe.3.36 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.ft.4.32 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.ln.3.36 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.lw.4.32 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.mp.2.37 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
312.384.9-312.my.3.38 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |