Invariants
Level: | $156$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $72$ | $\PSL_2$-index: | $36$ | ||||
Genus: | $1 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $6^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 36$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 6E1 |
Level structure
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}1&62\\14&11\end{bmatrix}$, $\begin{bmatrix}19&96\\92&59\end{bmatrix}$, $\begin{bmatrix}85&104\\0&155\end{bmatrix}$, $\begin{bmatrix}109&10\\112&153\end{bmatrix}$, $\begin{bmatrix}117&86\\122&49\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 78.36.1.a.1 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $112$ |
Cyclic 156-torsion field degree: | $5376$ |
Full 156-torsion field degree: | $1677312$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.36.1-6.a.1.2 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
156.36.1-6.a.1.4 | $156$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.144.3-156.i.1.2 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.i.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.k.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.k.1.6 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.k.1.12 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.m.1.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.m.1.6 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.m.1.8 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.o.1.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.o.1.6 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.o.1.7 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bg.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bg.1.5 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bg.1.7 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bh.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bh.1.6 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bh.1.7 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bk.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bk.1.5 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bk.1.8 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bl.1.2 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bl.1.3 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.144.3-156.bl.1.8 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.z.1.2 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.z.1.5 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.z.1.15 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bf.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bf.1.9 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bf.1.16 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bl.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bl.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.bl.1.15 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.br.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.br.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.br.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ds.1.5 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ds.1.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ds.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.dv.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.dv.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.dv.1.15 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ee.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ee.1.9 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.ee.1.16 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.eh.1.2 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.eh.1.5 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.144.3-312.eh.1.15 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |