Invariants
Level: | $88$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
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: | 8I0 |
Level structure
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 |
---|---|---|---|---|---|
$X_0(8)$ | $8$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
88.48.0.z.2 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bc.1 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bd.2 | $88$ | $2$ | $2$ | $0$ |
88.48.0.be.1 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bg.1 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bj.2 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bl.2 | $88$ | $2$ | $2$ | $0$ |
88.48.0.bm.2 | $88$ | $2$ | $2$ | $0$ |
88.288.19.fs.2 | $88$ | $12$ | $12$ | $19$ |
176.48.0.bc.1 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bi.1 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bk.2 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bq.2 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bs.1 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bu.1 | $176$ | $2$ | $2$ | $0$ |
176.48.0.bw.2 | $176$ | $2$ | $2$ | $0$ |
176.48.0.by.2 | $176$ | $2$ | $2$ | $0$ |
176.48.1.bg.2 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bi.2 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bk.1 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bm.1 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bo.2 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bu.2 | $176$ | $2$ | $2$ | $1$ |
176.48.1.bw.1 | $176$ | $2$ | $2$ | $1$ |
176.48.1.cc.1 | $176$ | $2$ | $2$ | $1$ |
264.48.0.de.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0.dg.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0.di.2 | $264$ | $2$ | $2$ | $0$ |
264.48.0.dk.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0.ea.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0.ef.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0.ej.2 | $264$ | $2$ | $2$ | $0$ |
264.48.0.em.1 | $264$ | $2$ | $2$ | $0$ |
264.72.4.no.1 | $264$ | $3$ | $3$ | $4$ |
264.96.3.ph.2 | $264$ | $4$ | $4$ | $3$ |