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: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}55&132\\148&97\end{bmatrix}$, $\begin{bmatrix}149&18\\104&269\end{bmatrix}$, $\begin{bmatrix}163&222\\124&191\end{bmatrix}$, $\begin{bmatrix}235&12\\86&133\end{bmatrix}$, $\begin{bmatrix}311&180\\64&223\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.lp.4 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 is an elliptic curve, but the rank has not been computed
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.2.14 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.4 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.o.2.33 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-312.dh.1.30 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dh.1.31 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.2.18 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.iw.4.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ix.4.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.jc.4.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kc.2.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ki.2.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kq.4.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.kw.4.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.og.3.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.oh.2.24 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ol.3.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.on.3.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pr.3.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ps.3.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qf.3.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qg.4.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |