Invariants
Level: | $156$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
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: | 12V1 |
Level structure
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}13&144\\94&145\end{bmatrix}$, $\begin{bmatrix}89&96\\136&19\end{bmatrix}$, $\begin{bmatrix}119&126\\46&41\end{bmatrix}$, $\begin{bmatrix}125&90\\22&125\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.96.1.f.4 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $28$ |
Cyclic 156-torsion field degree: | $672$ |
Full 156-torsion field degree: | $628992$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
156.96.0-12.a.2.13 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.96.0-156.a.1.2 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.96.0-156.a.1.9 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.96.1-156.b.1.4 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.b.1.6 | $156$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.384.5-156.g.1.2 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.h.4.3 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.m.3.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.o.3.4 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.q.2.2 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.r.3.2 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.w.3.1 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
156.384.5-156.y.1.1 | $156$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.iu.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ja.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ke.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ks.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.og.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.om.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.pq.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.qe.4.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |