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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}77&36\\130&21\end{bmatrix}$, $\begin{bmatrix}85&44\\8&39\end{bmatrix}$, $\begin{bmatrix}127&88\\122&49\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.96.1.t.2 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 |
---|---|---|---|---|---|---|
8.96.1-8.i.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
136.96.0-136.j.1.4 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.j.1.13 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.l.2.7 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.l.2.14 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.v.2.3 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.v.2.11 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.x.1.3 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.x.1.13 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.1-8.i.2.4 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.p.1.5 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.p.1.9 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.s.1.5 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.s.1.11 | $136$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
272.384.5-272.t.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.z.1.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.br.2.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.bs.2.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ei.2.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.ej.2.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.fa.1.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.fg.1.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.9-272.im.1.15 | $272$ | $2$ | $2$ | $9$ | $?$ | not computed |
272.384.9-272.in.1.15 | $272$ | $2$ | $2$ | $9$ | $?$ | not computed |
272.384.9-272.iv.1.15 | $272$ | $2$ | $2$ | $9$ | $?$ | not computed |
272.384.9-272.iw.1.15 | $272$ | $2$ | $2$ | $9$ | $?$ | not computed |