Invariants
| Level: | $88$ | $\SL_2$-level: | $8$ | ||||
| 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 | $1^{2}\cdot2\cdot8$ | 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: | 8C0 |
Level structure
| $\GL_2(\Z/88\Z)$-generators: | $\begin{bmatrix}27&56\\42&77\end{bmatrix}$, $\begin{bmatrix}41&16\\2&19\end{bmatrix}$, $\begin{bmatrix}41&86\\60&3\end{bmatrix}$, $\begin{bmatrix}84&79\\45&10\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.12.0.z.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.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 88.12.0-4.c.1.2 | $88$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 88.48.0-88.m.1.12 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.o.1.4 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.u.1.4 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.v.1.7 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bj.1.7 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bk.1.6 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bm.1.8 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0-88.bp.1.8 | $88$ | $2$ | $2$ | $0$ |
| 88.288.9-88.bn.1.28 | $88$ | $12$ | $12$ | $9$ |
| 264.48.0-264.br.1.16 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.bt.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.bz.1.16 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.cb.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.df.1.8 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.dg.1.14 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.dm.1.16 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0-264.dp.1.12 | $264$ | $2$ | $2$ | $0$ |
| 264.72.2-264.cv.1.62 | $264$ | $3$ | $3$ | $2$ |
| 264.96.1-264.zt.1.47 | $264$ | $4$ | $4$ | $1$ |