Invariants
Level: | $312$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}138&283\\191&124\end{bmatrix}$, $\begin{bmatrix}162&247\\293&136\end{bmatrix}$, $\begin{bmatrix}168&181\\101&310\end{bmatrix}$, $\begin{bmatrix}215&276\\150&83\end{bmatrix}$, $\begin{bmatrix}218&67\\171&292\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.24.1.hn.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $40255488$ |
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 |
---|---|---|---|---|---|---|
12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.24.0-6.a.1.8 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
312.96.1-312.dg.1.33 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.gf.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.kf.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.kg.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.yw.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.yx.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zf.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zg.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bkz.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bla.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blf.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blg.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bll.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blm.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blr.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bls.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.144.3-312.dit.1.3 | $312$ | $3$ | $3$ | $3$ | $?$ | not computed |