Invariants
Level: | $312$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}49&296\\96&185\end{bmatrix}$, $\begin{bmatrix}77&103\\218&171\end{bmatrix}$, $\begin{bmatrix}133&123\\204&7\end{bmatrix}$, $\begin{bmatrix}177&242\\250&131\end{bmatrix}$, $\begin{bmatrix}179&105\\152&265\end{bmatrix}$, $\begin{bmatrix}197&225\\80&247\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.caf.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $20127744$ |
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 |
---|---|---|---|---|---|---|
12.48.1-12.l.1.10 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
312.48.0-312.fr.1.5 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.fr.1.12 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.ft.1.2 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.ft.1.15 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.1-12.l.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.192.3-312.xy.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.xz.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yc.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yd.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zg.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zh.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zi.1.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zj.1.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zk.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zl.1.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zm.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zn.1.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zq.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zr.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zu.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.zv.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.5-312.ct.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.cv.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.js.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.jv.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.qa.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.qd.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.rh.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.rj.1.29 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.cai.1.1 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |