Invariants
Level: | $156$ | $\SL_2$-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
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}103&35\\66&125\end{bmatrix}$, $\begin{bmatrix}105&14\\64&29\end{bmatrix}$, $\begin{bmatrix}105&154\\82&51\end{bmatrix}$, $\begin{bmatrix}139&87\\6&73\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.48.1.bu.1 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $28$ |
Cyclic 156-torsion field degree: | $1344$ |
Full 156-torsion field degree: | $1257984$ |
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 |
78.48.0-78.c.1.3 | $78$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.0-78.c.1.12 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.0-156.s.1.11 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.0-156.s.1.16 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.1-12.l.1.3 | $156$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.192.3-156.cb.1.4 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.cc.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.cd.1.2 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.ce.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.288.5-156.gz.1.1 | $156$ | $3$ | $3$ | $5$ | $?$ | not computed |
312.192.3-312.xs.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.xt.1.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ye.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yf.1.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yi.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yj.1.10 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yk.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yl.1.10 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yu.1.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yv.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yy.1.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.yz.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.5-312.co.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.cq.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.jp.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.jq.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.px.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.py.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.rc.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.192.5-312.re.1.30 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |