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: | $16$ (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
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}11&40\\20&73\end{bmatrix}$, $\begin{bmatrix}41&24\\20&81\end{bmatrix}$, $\begin{bmatrix}47&20\\44&57\end{bmatrix}$, $\begin{bmatrix}51&84\\72&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.96.1.x.2 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $240$ |
Full 88-torsion field degree: | $105600$ |
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.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.96.0-8.c.1.3 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.b.1.1 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.b.1.22 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.u.2.5 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.u.2.12 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.v.2.6 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.0-88.v.2.11 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.96.1-88.o.2.8 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.o.2.14 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.be.1.2 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.be.1.15 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.bf.1.2 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.96.1-88.bf.1.11 | $88$ | $2$ | $2$ | $1$ | $?$ | 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.1.1 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.y.1.1 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.ba.1.1 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
88.384.5-88.bb.4.1 | $88$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.a.2.2 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.g.2.3 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.p.2.5 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.r.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cq.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cs.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.db.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.dh.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hi.1.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hk.1.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hs.1.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hu.2.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |