Invariants
Level: | $156$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $3^{8}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12S1 |
Level structure
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}11&76\\63&19\end{bmatrix}$, $\begin{bmatrix}53&52\\144&1\end{bmatrix}$, $\begin{bmatrix}109&102\\147&37\end{bmatrix}$, $\begin{bmatrix}121&62\\27&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.72.1.n.1 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $28$ |
Cyclic 156-torsion field degree: | $1344$ |
Full 156-torsion field degree: | $838656$ |
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 |
---|---|---|---|---|---|---|
12.72.0-6.a.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
156.48.0-156.q.1.3 | $156$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
156.48.0-156.q.1.7 | $156$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
156.72.0-6.a.1.1 | $156$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.288.5-156.b.1.6 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.bg.1.3 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.dt.1.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.dw.1.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.ek.1.3 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.eq.1.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.fg.1.6 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.288.5-156.fl.1.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.dd.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.it.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bdw.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.ber.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bik.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bka.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.boj.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bps.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |