Invariants
| Level: | $8$ | $\SL_2$-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 |
| Sutherland and Zywina (SZ) label: | 8I0-8b |
| Rouse and Zureick-Brown (RZB) label: | X86 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 8.24.0.91 |
Level structure
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 131 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2}{3^4}\cdot\frac{(6x-y)^{24}(78941952x^{8}-342641664x^{7}y+528705792x^{6}y^{2}-425440512x^{5}y^{3}+202292640x^{4}y^{4}-58888512x^{3}y^{5}+10248336x^{2}y^{6}-966192xy^{7}+37199y^{8})^{3}}{(2x-y)^{4}(6x-y)^{26}(36x^{2}-24xy+5y^{2})(108x^{2}-60xy+11y^{2})^{8}}$ |
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
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 |
|---|---|---|---|---|
| 8.48.0.j.2 | $8$ | $2$ | $2$ | $0$ |
| 8.48.0.m.1 | $8$ | $2$ | $2$ | $0$ |
| 8.48.0.n.1 | $8$ | $2$ | $2$ | $0$ |
| 8.48.0.o.1 | $8$ | $2$ | $2$ | $0$ |
| 16.48.0.u.2 | $16$ | $2$ | $2$ | $0$ |
| 16.48.0.w.2 | $16$ | $2$ | $2$ | $0$ |
| 16.48.0.y.2 | $16$ | $2$ | $2$ | $0$ |
| 16.48.0.ba.2 | $16$ | $2$ | $2$ | $0$ |
| 16.48.1.q.2 | $16$ | $2$ | $2$ | $1$ |
| 16.48.1.s.2 | $16$ | $2$ | $2$ | $1$ |
| 16.48.1.u.2 | $16$ | $2$ | $2$ | $1$ |
| 16.48.1.w.2 | $16$ | $2$ | $2$ | $1$ |
| 24.48.0.bi.1 | $24$ | $2$ | $2$ | $0$ |
| 24.48.0.bk.2 | $24$ | $2$ | $2$ | $0$ |
| 24.48.0.bm.2 | $24$ | $2$ | $2$ | $0$ |
| 24.48.0.bo.2 | $24$ | $2$ | $2$ | $0$ |
| 24.72.4.ge.2 | $24$ | $3$ | $3$ | $4$ |
| 24.96.3.gf.1 | $24$ | $4$ | $4$ | $3$ |
| 40.48.0.bi.2 | $40$ | $2$ | $2$ | $0$ |
| 40.48.0.bk.2 | $40$ | $2$ | $2$ | $0$ |
| 40.48.0.bm.2 | $40$ | $2$ | $2$ | $0$ |
| 40.48.0.bo.1 | $40$ | $2$ | $2$ | $0$ |
| 40.120.8.da.1 | $40$ | $5$ | $5$ | $8$ |
| 40.144.7.fn.1 | $40$ | $6$ | $6$ | $7$ |
| 40.240.15.gq.1 | $40$ | $10$ | $10$ | $15$ |
| 48.48.0.be.2 | $48$ | $2$ | $2$ | $0$ |
| 48.48.0.bg.2 | $48$ | $2$ | $2$ | $0$ |
| 48.48.0.bm.1 | $48$ | $2$ | $2$ | $0$ |
| 48.48.0.bo.2 | $48$ | $2$ | $2$ | $0$ |
| 48.48.1.bq.2 | $48$ | $2$ | $2$ | $1$ |
| 48.48.1.bs.1 | $48$ | $2$ | $2$ | $1$ |
| 48.48.1.by.2 | $48$ | $2$ | $2$ | $1$ |
| 48.48.1.ca.2 | $48$ | $2$ | $2$ | $1$ |
| 56.48.0.bg.2 | $56$ | $2$ | $2$ | $0$ |
| 56.48.0.bi.2 | $56$ | $2$ | $2$ | $0$ |
| 56.48.0.bk.2 | $56$ | $2$ | $2$ | $0$ |
| 56.48.0.bm.2 | $56$ | $2$ | $2$ | $0$ |
| 56.192.11.fb.1 | $56$ | $8$ | $8$ | $11$ |
| 56.504.34.ge.2 | $56$ | $21$ | $21$ | $34$ |
| 56.672.45.gq.1 | $56$ | $28$ | $28$ | $45$ |
| 80.48.0.bm.2 | $80$ | $2$ | $2$ | $0$ |
| 80.48.0.bo.1 | $80$ | $2$ | $2$ | $0$ |
| 80.48.0.bu.1 | $80$ | $2$ | $2$ | $0$ |
| 80.48.0.bw.1 | $80$ | $2$ | $2$ | $0$ |
| 80.48.1.bs.1 | $80$ | $2$ | $2$ | $1$ |
| 80.48.1.bu.1 | $80$ | $2$ | $2$ | $1$ |
| 80.48.1.ca.1 | $80$ | $2$ | $2$ | $1$ |
| 80.48.1.cc.2 | $80$ | $2$ | $2$ | $1$ |
| 88.48.0.bg.2 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0.bi.2 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0.bk.2 | $88$ | $2$ | $2$ | $0$ |
| 88.48.0.bm.2 | $88$ | $2$ | $2$ | $0$ |
| 88.288.19.fr.1 | $88$ | $12$ | $12$ | $19$ |
| 104.48.0.bi.2 | $104$ | $2$ | $2$ | $0$ |
| 104.48.0.bk.2 | $104$ | $2$ | $2$ | $0$ |
| 104.48.0.bm.2 | $104$ | $2$ | $2$ | $0$ |
| 104.48.0.bo.1 | $104$ | $2$ | $2$ | $0$ |
| 104.336.23.fn.1 | $104$ | $14$ | $14$ | $23$ |
| 112.48.0.be.2 | $112$ | $2$ | $2$ | $0$ |
| 112.48.0.bg.1 | $112$ | $2$ | $2$ | $0$ |
| 112.48.0.bm.1 | $112$ | $2$ | $2$ | $0$ |
| 112.48.0.bo.1 | $112$ | $2$ | $2$ | $0$ |
| 112.48.1.bq.1 | $112$ | $2$ | $2$ | $1$ |
| 112.48.1.bs.1 | $112$ | $2$ | $2$ | $1$ |
| 112.48.1.by.1 | $112$ | $2$ | $2$ | $1$ |
| 112.48.1.ca.2 | $112$ | $2$ | $2$ | $1$ |
| 120.48.0.ed.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.eh.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.el.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.ep.2 | $120$ | $2$ | $2$ | $0$ |
| 136.48.0.bi.2 | $136$ | $2$ | $2$ | $0$ |
| 136.48.0.bk.2 | $136$ | $2$ | $2$ | $0$ |
| 136.48.0.bm.2 | $136$ | $2$ | $2$ | $0$ |
| 136.48.0.bo.2 | $136$ | $2$ | $2$ | $0$ |
| 152.48.0.bg.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0.bi.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0.bk.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0.bm.2 | $152$ | $2$ | $2$ | $0$ |
| 168.48.0.dz.2 | $168$ | $2$ | $2$ | $0$ |
| 168.48.0.ed.2 | $168$ | $2$ | $2$ | $0$ |
| 168.48.0.eh.2 | $168$ | $2$ | $2$ | $0$ |
| 168.48.0.el.2 | $168$ | $2$ | $2$ | $0$ |
| 176.48.0.be.2 | $176$ | $2$ | $2$ | $0$ |
| 176.48.0.bg.2 | $176$ | $2$ | $2$ | $0$ |
| 176.48.0.bm.1 | $176$ | $2$ | $2$ | $0$ |
| 176.48.0.bo.1 | $176$ | $2$ | $2$ | $0$ |
| 176.48.1.bq.1 | $176$ | $2$ | $2$ | $1$ |
| 176.48.1.bs.1 | $176$ | $2$ | $2$ | $1$ |
| 176.48.1.by.2 | $176$ | $2$ | $2$ | $1$ |
| 176.48.1.ca.2 | $176$ | $2$ | $2$ | $1$ |
| 184.48.0.bg.2 | $184$ | $2$ | $2$ | $0$ |
| 184.48.0.bi.2 | $184$ | $2$ | $2$ | $0$ |
| 184.48.0.bk.2 | $184$ | $2$ | $2$ | $0$ |
| 184.48.0.bm.2 | $184$ | $2$ | $2$ | $0$ |
| 208.48.0.bm.2 | $208$ | $2$ | $2$ | $0$ |
| 208.48.0.bo.2 | $208$ | $2$ | $2$ | $0$ |
| 208.48.0.bu.1 | $208$ | $2$ | $2$ | $0$ |
| 208.48.0.bw.1 | $208$ | $2$ | $2$ | $0$ |
| 208.48.1.bs.1 | $208$ | $2$ | $2$ | $1$ |
| 208.48.1.bu.1 | $208$ | $2$ | $2$ | $1$ |
| 208.48.1.ca.2 | $208$ | $2$ | $2$ | $1$ |
| 208.48.1.cc.2 | $208$ | $2$ | $2$ | $1$ |
| 232.48.0.bi.2 | $232$ | $2$ | $2$ | $0$ |
| 232.48.0.bk.2 | $232$ | $2$ | $2$ | $0$ |
| 232.48.0.bm.2 | $232$ | $2$ | $2$ | $0$ |
| 232.48.0.bo.2 | $232$ | $2$ | $2$ | $0$ |
| 240.48.0.co.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cq.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.de.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.dg.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.1.fo.2 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.fq.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ge.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.gg.2 | $240$ | $2$ | $2$ | $1$ |
| 248.48.0.bg.2 | $248$ | $2$ | $2$ | $0$ |
| 248.48.0.bi.2 | $248$ | $2$ | $2$ | $0$ |
| 248.48.0.bk.2 | $248$ | $2$ | $2$ | $0$ |
| 248.48.0.bm.2 | $248$ | $2$ | $2$ | $0$ |
| 264.48.0.dz.2 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0.ed.2 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0.eh.1 | $264$ | $2$ | $2$ | $0$ |
| 264.48.0.el.2 | $264$ | $2$ | $2$ | $0$ |
| 272.48.0.bm.1 | $272$ | $2$ | $2$ | $0$ |
| 272.48.0.bo.1 | $272$ | $2$ | $2$ | $0$ |
| 272.48.0.bu.2 | $272$ | $2$ | $2$ | $0$ |
| 272.48.0.bw.2 | $272$ | $2$ | $2$ | $0$ |
| 272.48.1.bs.2 | $272$ | $2$ | $2$ | $1$ |
| 272.48.1.bu.2 | $272$ | $2$ | $2$ | $1$ |
| 272.48.1.ca.1 | $272$ | $2$ | $2$ | $1$ |
| 272.48.1.cc.1 | $272$ | $2$ | $2$ | $1$ |
| 280.48.0.dw.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0.ea.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0.ee.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0.ei.2 | $280$ | $2$ | $2$ | $0$ |
| 296.48.0.bi.2 | $296$ | $2$ | $2$ | $0$ |
| 296.48.0.bk.2 | $296$ | $2$ | $2$ | $0$ |
| 296.48.0.bm.2 | $296$ | $2$ | $2$ | $0$ |
| 296.48.0.bo.1 | $296$ | $2$ | $2$ | $0$ |
| 304.48.0.be.2 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0.bg.2 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0.bm.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0.bo.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.1.bq.1 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1.bs.1 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1.by.2 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1.ca.2 | $304$ | $2$ | $2$ | $1$ |
| 312.48.0.ed.2 | $312$ | $2$ | $2$ | $0$ |
| 312.48.0.eh.2 | $312$ | $2$ | $2$ | $0$ |
| 312.48.0.el.2 | $312$ | $2$ | $2$ | $0$ |
| 312.48.0.ep.2 | $312$ | $2$ | $2$ | $0$ |
| 328.48.0.bi.2 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0.bk.2 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0.bm.2 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0.bo.2 | $328$ | $2$ | $2$ | $0$ |