Invariants
Level: | $136$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{4}$ | ||
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: | 8B1 |
Level structure
$\GL_2(\Z/136\Z)$-generators: | $\begin{bmatrix}37&64\\24&109\end{bmatrix}$, $\begin{bmatrix}47&4\\20&77\end{bmatrix}$, $\begin{bmatrix}61&90\\100&13\end{bmatrix}$, $\begin{bmatrix}79&124\\92&49\end{bmatrix}$, $\begin{bmatrix}111&44\\28&23\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.24.1.c.1 for the level structure with $-I$) |
Cyclic 136-isogeny field degree: | $36$ |
Cyclic 136-torsion field degree: | $2304$ |
Full 136-torsion field degree: | $2506752$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.b.1.9 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
68.24.0-4.b.1.3 | $68$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
136.96.1-136.o.2.3 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.v.1.5 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bc.1.15 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bc.2.16 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bd.1.13 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bd.2.9 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.be.1.15 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.be.2.13 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bf.1.16 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bf.2.14 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bt.1.5 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.96.1-136.bu.1.3 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |