Invariants
Level: | $136$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-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: | $\begin{bmatrix}7&36\\40&47\end{bmatrix}$, $\begin{bmatrix}35&36\\128&71\end{bmatrix}$, $\begin{bmatrix}87&112\\116&103\end{bmatrix}$, $\begin{bmatrix}101&48\\96&31\end{bmatrix}$, $\begin{bmatrix}125&108\\80&95\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 136.192.1-136.w.2.1, 136.192.1-136.w.2.2, 136.192.1-136.w.2.3, 136.192.1-136.w.2.4, 136.192.1-136.w.2.5, 136.192.1-136.w.2.6, 136.192.1-136.w.2.7, 136.192.1-136.w.2.8, 136.192.1-136.w.2.9, 136.192.1-136.w.2.10, 136.192.1-136.w.2.11, 136.192.1-136.w.2.12, 272.192.1-136.w.2.1, 272.192.1-136.w.2.2, 272.192.1-136.w.2.3, 272.192.1-136.w.2.4, 272.192.1-136.w.2.5, 272.192.1-136.w.2.6, 272.192.1-136.w.2.7, 272.192.1-136.w.2.8 |
Cyclic 136-isogeny field degree: | $36$ |
Cyclic 136-torsion field degree: | $1152$ |
Full 136-torsion field degree: | $1253376$ |
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 |
---|---|---|---|---|---|---|
8.48.0.c.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.48.0.b.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.0.s.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.0.t.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.1.n.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.48.1.bi.1 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.48.1.bj.1 | $136$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
136.192.5.w.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.192.5.y.2 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.192.5.z.1 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
136.192.5.bb.2 | $136$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.c.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.e.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.bf.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.bl.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.em.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.es.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.ft.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |
272.192.5.fv.2 | $272$ | $2$ | $2$ | $5$ | $?$ | not computed |