Invariants
Level: | $136$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/136\Z)$-generators: | $\begin{bmatrix}5&108\\72&1\end{bmatrix}$, $\begin{bmatrix}7&124\\36&65\end{bmatrix}$, $\begin{bmatrix}67&26\\0&39\end{bmatrix}$, $\begin{bmatrix}127&104\\44&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 136.48.1.be.2 for the level structure with $-I$) |
Cyclic 136-isogeny field degree: | $36$ |
Cyclic 136-torsion field degree: | $2304$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
136.48.0-8.e.1.9 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.0-136.h.1.2 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.0-136.h.1.18 | $136$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
136.48.1-136.c.1.6 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.48.1-136.c.1.20 | $136$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
136.192.1-136.h.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.x.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.bd.1.3 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.bh.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.bv.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.bz.1.3 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.cb.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
136.192.1-136.cd.1.2 | $136$ | $2$ | $2$ | $1$ | $?$ | dimension zero |