Invariants
Level: | $88$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G0 |
Level structure
$\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}11&60\\43&17\end{bmatrix}$, $\begin{bmatrix}21&36\\48&9\end{bmatrix}$, $\begin{bmatrix}25&80\\43&7\end{bmatrix}$, $\begin{bmatrix}37&64\\9&3\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.24.0.t.1 for the level structure with $-I$) |
Cyclic 88-isogeny field degree: | $24$ |
Cyclic 88-torsion field degree: | $960$ |
Full 88-torsion field degree: | $422400$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
44.24.0-4.d.1.1 | $44$ | $2$ | $2$ | $0$ | $0$ |
88.24.0-88.y.1.1 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.24.0-88.y.1.3 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.24.0-88.y.1.14 | $88$ | $2$ | $2$ | $0$ | $?$ |
88.24.0-88.y.1.16 | $88$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
88.96.1-88.dg.1.3 | $88$ | $2$ | $2$ | $1$ |
88.96.1-88.dh.1.4 | $88$ | $2$ | $2$ | $1$ |
88.96.1-88.di.1.4 | $88$ | $2$ | $2$ | $1$ |
88.96.1-88.dj.1.4 | $88$ | $2$ | $2$ | $1$ |
264.96.1-264.ki.1.8 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.kj.1.5 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.kk.1.8 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.kl.1.8 | $264$ | $2$ | $2$ | $1$ |
264.144.4-264.fs.1.9 | $264$ | $3$ | $3$ | $4$ |
264.192.3-264.hg.1.29 | $264$ | $4$ | $4$ | $3$ |