Invariants
Level: | $80$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2\cdot4$ | ||
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: | 4G0 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}44&49\\65&62\end{bmatrix}$, $\begin{bmatrix}44&75\\21&58\end{bmatrix}$, $\begin{bmatrix}73&62\\50&39\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.24.0.i.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $48$ |
Cyclic 80-torsion field degree: | $1536$ |
Full 80-torsion field degree: | $245760$ |
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 |
---|---|---|---|---|---|
40.24.0-40.p.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
80.24.0-40.p.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
80.240.8-80.m.1.4 | $80$ | $5$ | $5$ | $8$ |
80.288.7-80.ba.1.8 | $80$ | $6$ | $6$ | $7$ |
80.480.15-80.y.1.10 | $80$ | $10$ | $10$ | $15$ |
240.144.4-240.bg.1.7 | $240$ | $3$ | $3$ | $4$ |
240.192.3-240.cgz.1.12 | $240$ | $4$ | $4$ | $3$ |