Invariants
Level: | $88$ | $\SL_2$-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: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}25&64\\64&19\end{bmatrix}$, $\begin{bmatrix}39&48\\20&45\end{bmatrix}$, $\begin{bmatrix}49&36\\0&29\end{bmatrix}$, $\begin{bmatrix}57&16\\52&85\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.96.1.x.1 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $480$ |
Full 88-torsion field degree: | $105600$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
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.1.8 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.96.0-88.b.2.7 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.b.2.15 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-8.c.1.7 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.1-88.o.2.21 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.o.2.22 | $88$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
88.384.5-88.x.1.3 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.x.1.5 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.y.2.2 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.y.2.5 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.ba.2.4 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.ba.2.7 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.bb.3.3 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.bb.3.5 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.a.1.12 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.a.1.15 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.g.1.11 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.g.1.13 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.p.1.11 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.p.1.16 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.r.1.9 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.r.1.15 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cq.1.11 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cq.1.13 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cs.1.12 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cs.1.14 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.db.1.9 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.db.1.15 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.dh.1.10 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.dh.1.16 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hi.2.5 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hi.2.11 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hk.2.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hk.2.14 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hs.2.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hs.2.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hu.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hu.1.9 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |