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: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-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: | $\begin{bmatrix}4&63\\15&68\end{bmatrix}$, $\begin{bmatrix}15&8\\2&37\end{bmatrix}$, $\begin{bmatrix}20&31\\29&62\end{bmatrix}$, $\begin{bmatrix}47&12\\40&27\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.0.bu.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $192$ |
Full 80-torsion field degree: | $122880$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
16.48.0-8.ba.2.4 | $16$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-8.ba.2.8 | $40$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-80.m.1.17 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.m.1.22 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.p.1.19 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-80.p.1.21 | $80$ | $2$ | $2$ | $0$ | $?$ |
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.2.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.z.1.1 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.bi.2.7 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.bx.2.2 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.cg.2.5 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.cq.1.5 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.cu.2.2 | $80$ | $2$ | $2$ | $1$ |
80.192.1-80.di.2.2 | $80$ | $2$ | $2$ | $1$ |
80.480.16-80.co.1.9 | $80$ | $5$ | $5$ | $16$ |
240.192.1-240.qr.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rh.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rx.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.sn.2.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.tf.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.tt.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.uj.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.vb.2.2 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.wk.1.19 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.bap.1.33 | $240$ | $4$ | $4$ | $7$ |