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: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
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: | 8K1 |
Level structure
$\GL_2(\Z/136\Z)$-generators: | $\begin{bmatrix}5&84\\92&57\end{bmatrix}$, $\begin{bmatrix}7&0\\64&57\end{bmatrix}$, $\begin{bmatrix}21&32\\20&9\end{bmatrix}$, $\begin{bmatrix}49&16\\36&121\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.96.1.x.2 for the level structure with $-I$) |
Cyclic 136-isogeny field degree: | $36$ |
Cyclic 136-torsion field degree: | $576$ |
Full 136-torsion field degree: | $626688$ |
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 |
---|---|---|---|---|---|---|
8.96.0-8.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.96.0-136.b.1.1 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.b.1.14 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-8.c.1.3 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.w.2.7 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.w.2.10 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.x.2.6 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.x.2.9 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.1-136.o.2.8 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.o.2.14 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.be.1.1 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.be.1.16 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bf.1.1 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bf.1.13 | $136$ | $2$ | $2$ | $1$ | $?$ | 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.x.1.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.y.1.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.ba.1.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.384.5-136.bb.4.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.a.2.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.g.2.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.bh.2.6 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.bj.2.6 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.eo.2.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.eq.2.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.fr.2.5 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.fx.2.1 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |