Invariants
Level: | $156$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}10&77\\69&74\end{bmatrix}$, $\begin{bmatrix}39&20\\22&59\end{bmatrix}$, $\begin{bmatrix}124&69\\115&50\end{bmatrix}$, $\begin{bmatrix}151&86\\96&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.24.1.p.1 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $28$ |
Cyclic 156-torsion field degree: | $1344$ |
Full 156-torsion field degree: | $2515968$ |
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 |
---|---|---|---|---|---|---|
12.24.0-6.a.1.4 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
156.24.0-6.a.1.7 | $156$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.96.1-156.a.1.16 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.h.1.11 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.i.1.10 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.l.1.7 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.z.1.3 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.bb.1.6 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.bd.1.7 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.bf.1.3 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.144.3-156.mb.1.8 | $156$ | $3$ | $3$ | $3$ | $?$ | not computed |
312.96.1-312.gm.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.kh.1.14 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.yy.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zh.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blb.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blh.1.12 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bln.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.blt.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |