Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $4\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16I3 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}17&46\\2&67\end{bmatrix}$, $\begin{bmatrix}45&62\\6&7\end{bmatrix}$, $\begin{bmatrix}55&22\\57&69\end{bmatrix}$, $\begin{bmatrix}59&0\\1&69\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 80.192.3-80.xs.1.1, 80.192.3-80.xs.1.2, 80.192.3-80.xs.1.3, 80.192.3-80.xs.1.4, 240.192.3-80.xs.1.1, 240.192.3-80.xs.1.2, 240.192.3-80.xs.1.3, 240.192.3-80.xs.1.4 |
Cyclic 80-isogeny field degree: | $48$ |
Cyclic 80-torsion field degree: | $1536$ |
Full 80-torsion field degree: | $122880$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.1.cd.1 | $16$ | $2$ | $2$ | $1$ | $1$ |
40.48.1.jd.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
80.48.0.cp.1 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.1.fv.1 | $80$ | $2$ | $2$ | $1$ | $?$ |
80.48.2.cp.2 | $80$ | $2$ | $2$ | $2$ | $?$ |
80.48.2.dx.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
80.48.2.fd.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
240.288.19.bzor.1 | $240$ | $3$ | $3$ | $19$ |
240.384.21.jip.1 | $240$ | $4$ | $4$ | $21$ |