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: | $\begin{bmatrix}67&0\\269&1\end{bmatrix}$, $\begin{bmatrix}109&192\\75&5\end{bmatrix}$, $\begin{bmatrix}205&132\\172&127\end{bmatrix}$, $\begin{bmatrix}229&168\\170&55\end{bmatrix}$, $\begin{bmatrix}307&240\\56&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.ry.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 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.c.3.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.96.0-12.c.3.4 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.ds.4.14 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.ds.4.57 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-312.zo.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zo.1.24 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.bbp.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bbu.4.22 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bcn.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bcs.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bcw.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bcz.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bde.4.8 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bdh.4.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bik.1.4 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bin.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bji.4.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bjl.4.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bjp.4.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bju.4.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bjx.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bkc.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |