Invariants
| Level: | $88$ | $\SL_2$-level: | $88$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot11^{2}\cdot22\cdot88$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 88B9 |
Level structure
| $\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}2&77\\1&34\end{bmatrix}$, $\begin{bmatrix}5&0\\72&21\end{bmatrix}$, $\begin{bmatrix}57&72\\70&15\end{bmatrix}$, $\begin{bmatrix}65&4\\42&71\end{bmatrix}$, $\begin{bmatrix}74&17\\83&52\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.144.9.bk.1 for the level structure with $-I$) |
| Cyclic 88-isogeny field degree: | $2$ |
| Cyclic 88-torsion field degree: | $40$ |
| Full 88-torsion field degree: | $70400$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.m.1.8 | $8$ | $12$ | $12$ | $0$ | $0$ |
| $X_0(11)$ | $11$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.m.1.8 | $8$ | $12$ | $12$ | $0$ | $0$ |
| 44.144.4-44.c.1.5 | $44$ | $2$ | $2$ | $4$ | $0$ |
| 88.144.4-44.c.1.22 | $88$ | $2$ | $2$ | $4$ | $?$ |