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: | 8G1 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}7&58\\8&41\end{bmatrix}$, $\begin{bmatrix}71&70\\32&47\end{bmatrix}$, $\begin{bmatrix}83&8\\0&17\end{bmatrix}$, $\begin{bmatrix}83&26\\4&7\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.1.be.2 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $960$ |
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.e.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
88.48.0-8.e.1.3 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.0-88.h.1.14 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.0-88.h.1.26 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
88.48.1-88.c.1.9 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.48.1-88.c.1.16 | $88$ | $2$ | $2$ | $1$ | $?$ | 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.h.1.5 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.x.1.5 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.bd.1.5 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.bh.1.3 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.bv.1.7 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.bz.2.6 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cb.1.6 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
88.192.1-88.cd.1.6 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.fw.1.7 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.gc.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.hd.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.hj.2.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.mf.2.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ml.2.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.nl.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.nr.2.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.288.9-264.rr.2.36 | $264$ | $3$ | $3$ | $9$ | $?$ | not computed |
264.384.9-264.jj.2.37 | $264$ | $4$ | $4$ | $9$ | $?$ | not computed |