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: | $\begin{bmatrix}22&35\\177&38\end{bmatrix}$, $\begin{bmatrix}114&167\\31&200\end{bmatrix}$, $\begin{bmatrix}226&213\\159&190\end{bmatrix}$, $\begin{bmatrix}256&35\\297&188\end{bmatrix}$, $\begin{bmatrix}284&217\\257&300\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.24.1.hm.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
3.8.0-3.a.1.1 | $3$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
104.6.0.e.1 | $104$ | $8$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
6.24.0-6.a.1.2 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.24.0-6.a.1.9 | $312$ | $2$ | $2$ | $0$ | $?$ | 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.dh.1.8 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.gg.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.jw.1.24 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.jx.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.yz.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.za.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zc.1.24 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zd.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bkw.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bkx.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blc.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bld.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bli.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blj.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blo.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blp.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.144.3-312.diq.1.1 | $312$ | $3$ | $3$ | $3$ | $?$ | not computed |