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: | $\begin{bmatrix}51&72\\122&83\end{bmatrix}$, $\begin{bmatrix}99&32\\42&23\end{bmatrix}$, $\begin{bmatrix}135&60\\88&133\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.96.1.ch.1 for the level structure with $-I$) |
Cyclic 136-isogeny field degree: | $18$ |
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 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.l.1.4 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.96.0-8.l.1.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.o.2.4 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.o.2.16 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.p.2.6 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.p.2.13 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.bc.2.8 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.0-136.bc.2.16 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.96.1-136.bi.2.4 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bi.2.10 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bj.2.14 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bj.2.16 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bv.1.11 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bv.1.16 | $136$ | $2$ | $2$ | $1$ | $?$ | 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.dd.1.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.eb.1.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gb.2.12 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gc.1.6 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gj.2.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gk.1.9 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gv.1.10 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.gw.1.13 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hd.2.14 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.he.1.7 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hm.1.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.384.5-272.hu.1.8 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |