Invariants
Level: | $88$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8N0 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}7&78\\40&3\end{bmatrix}$, $\begin{bmatrix}9&38\\12&45\end{bmatrix}$, $\begin{bmatrix}43&12\\76&5\end{bmatrix}$, $\begin{bmatrix}67&36\\68&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.48.0.l.1 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $480$ |
Full 88-torsion field degree: | $211200$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.d.1.13 | $8$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-8.d.1.11 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.e.1.13 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.e.1.20 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.2.16 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.48.0-88.i.2.26 | $88$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
88.192.1-88.d.1.2 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.u.1.3 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.bi.2.5 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.bm.1.2 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.bt.2.6 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.bx.1.4 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.ce.1.4 | $88$ | $2$ | $2$ | $1$ |
88.192.1-88.cg.2.6 | $88$ | $2$ | $2$ | $1$ |
264.192.1-264.gj.2.15 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.gp.1.4 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ho.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.hu.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mr.1.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.mx.1.7 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.nx.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.od.1.14 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.ci.2.59 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.ck.2.57 | $264$ | $4$ | $4$ | $7$ |