Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16H0 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}8&73\\59&70\end{bmatrix}$, $\begin{bmatrix}20&13\\27&54\end{bmatrix}$, $\begin{bmatrix}30&7\\59&66\end{bmatrix}$, $\begin{bmatrix}56&31\\45&66\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.0.bw.2 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $192$ |
Full 80-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-8.ba.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-8.ba.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-80.n.1.6 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.n.1.17 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.p.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.p.1.11 | $80$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
80.192.1-80.d.1.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.ba.2.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.bm.2.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.bx.2.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.ce.1.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.cs.1.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.cw.2.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.dg.2.1 | $80$ | $2$ | $2$ | $1$ |
80.480.16-80.cq.2.1 | $80$ | $5$ | $5$ | $16$ |
240.192.1-240.qt.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rj.1.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rz.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.sp.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.td.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.tv.1.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ul.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.uz.1.1 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.xg.1.3 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.bav.1.1 | $240$ | $4$ | $4$ | $7$ |