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: | $\begin{bmatrix}18&29\\41&120\end{bmatrix}$, $\begin{bmatrix}19&18\\12&13\end{bmatrix}$, $\begin{bmatrix}76&107\\61&42\end{bmatrix}$, $\begin{bmatrix}108&115\\89&52\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.24.1.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: | $2515968$ |
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 |
---|---|---|---|---|---|---|
6.24.0-6.a.1.3 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
156.24.0-6.a.1.12 | $156$ | $2$ | $2$ | $0$ | $?$ | 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.c.1.9 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.g.1.2 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.m.1.1 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.p.1.4 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.q.1.5 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.t.1.1 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.u.1.1 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.96.1-156.x.1.5 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.144.3-156.jw.1.4 | $156$ | $3$ | $3$ | $3$ | $?$ | not computed |
312.96.1-312.gk.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ke.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zk.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.zt.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bae.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ban.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.baq.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.baz.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |