Invariants
Level: | $88$ | $\SL_2$-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: | 8F1 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}13&36\\80&59\end{bmatrix}$, $\begin{bmatrix}33&68\\40&87\end{bmatrix}$, $\begin{bmatrix}41&32\\58&13\end{bmatrix}$, $\begin{bmatrix}81&80\\16&21\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.1.bu.1 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $12$ |
Cyclic 88-torsion field degree: | $480$ |
Full 88-torsion field degree: | $211200$ |
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.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
44.48.0-44.c.1.3 | $44$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.48.0-44.c.1.13 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.0-8.i.1.8 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.1-88.c.1.6 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.48.1-88.c.1.17 | $88$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
88.192.1-88.ca.1.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.ca.2.7 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cb.1.1 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cb.2.2 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cc.1.2 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cc.2.4 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cd.1.1 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cd.2.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
176.192.3-176.bo.1.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.bo.2.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.cb.1.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.cb.2.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.ci.1.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.ci.2.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.cu.1.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
176.192.3-176.cu.2.6 | $176$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.1-264.os.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.os.2.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ot.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ot.2.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ou.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ou.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ov.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ov.2.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.288.9-264.bbe.1.57 | $264$ | $3$ | $3$ | $9$ | $?$ | not computed |
264.384.9-264.oi.1.53 | $264$ | $4$ | $4$ | $9$ | $?$ | not computed |