Invariants
Level: | $136$ | $\SL_2$-level: | $8$ | 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: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/136\Z)$-generators: | $\begin{bmatrix}1&72\\96&85\end{bmatrix}$, $\begin{bmatrix}97&20\\20&127\end{bmatrix}$, $\begin{bmatrix}113&60\\24&115\end{bmatrix}$, $\begin{bmatrix}119&120\\76&125\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.96.1.w.1 for the level structure with $-I$) |
Cyclic 136-isogeny field degree: | $36$ |
Cyclic 136-torsion field degree: | $1152$ |
Full 136-torsion field degree: | $626688$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.0-8.c.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.96.0-136.b.1.9 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.b.1.13 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-8.c.1.9 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.s.1.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.s.1.11 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.t.1.5 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.t.1.16 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.1-136.n.2.3 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.n.2.4 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bi.2.5 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bi.2.8 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bj.2.4 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bj.2.9 | $136$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
136.384.5-136.w.1.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.y.1.3 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.z.2.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.bb.1.3 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.c.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.e.1.3 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.bf.1.6 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.bl.1.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.em.1.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.es.1.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ft.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.fv.1.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |