Invariants
Level: | $156$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/156\Z)$-generators: | $\begin{bmatrix}3&88\\142&57\end{bmatrix}$, $\begin{bmatrix}3&110\\44&69\end{bmatrix}$, $\begin{bmatrix}7&86\\112&129\end{bmatrix}$, $\begin{bmatrix}49&90\\148&155\end{bmatrix}$, $\begin{bmatrix}155&36\\78&119\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 156.48.1.a.1 for the level structure with $-I$) |
Cyclic 156-isogeny field degree: | $28$ |
Cyclic 156-torsion field degree: | $1344$ |
Full 156-torsion field degree: | $1257984$ |
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 |
---|---|---|---|---|---|---|
12.48.0-6.a.1.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
78.48.0-6.a.1.2 | $78$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.0-156.p.1.5 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.0-156.p.1.12 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
156.48.1-156.p.1.6 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.48.1-156.p.1.11 | $156$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
156.192.1-156.e.1.7 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.192.1-156.e.2.7 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.192.1-156.e.3.5 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.192.1-156.e.4.5 | $156$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
156.192.3-156.a.1.9 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.c.1.14 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.g.1.10 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.i.1.10 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.o.1.10 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.o.2.12 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.s.1.12 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.192.3-156.s.2.9 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
156.288.5-156.a.1.5 | $156$ | $3$ | $3$ | $5$ | $?$ | not computed |
312.192.1-312.ln.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ln.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ln.3.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ln.4.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.3-312.dp.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.dt.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ed.1.20 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ej.1.20 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.fl.1.18 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.fl.2.20 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ge.1.20 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ge.2.18 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |