Invariants
| Level: | $88$ | $\SL_2$-level: | $4$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4E0 |
Level structure
| $\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}3&60\\32&17\end{bmatrix}$, $\begin{bmatrix}5&4\\17&45\end{bmatrix}$, $\begin{bmatrix}13&68\\9&43\end{bmatrix}$, $\begin{bmatrix}27&80\\64&57\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.12.0.s.1 for the level structure with $-I$) |
| Cyclic 88-isogeny field degree: | $24$ |
| Cyclic 88-torsion field degree: | $960$ |
| Full 88-torsion field degree: | $844800$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 44.12.0-4.c.1.2 | $44$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 88.48.0-88.bg.1.4 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bg.1.5 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bh.1.1 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bh.1.8 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bo.1.3 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bo.1.6 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bp.1.2 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bp.1.7 | $88$ | $2$ | $2$ | $0$ |
| 88.288.9-88.be.1.2 | $88$ | $12$ | $12$ | $9$ |
| 264.48.0-264.ci.1.6 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.ci.1.11 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cj.1.5 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cj.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cq.1.8 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cq.1.9 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cr.1.7 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cr.1.10 | $264$ | $2$ | $2$ | $0$ |
| 264.72.2-264.cc.1.9 | $264$ | $3$ | $3$ | $2$ |
| 264.96.1-264.za.1.9 | $264$ | $4$ | $4$ | $1$ |