Invariants
Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $10^{8}\cdot80^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 80A16 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}15&71\\36&47\end{bmatrix}$, $\begin{bmatrix}19&32\\56&11\end{bmatrix}$, $\begin{bmatrix}49&2\\44&11\end{bmatrix}$, $\begin{bmatrix}59&59\\24&21\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.240.16.k.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $192$ |
Full 80-torsion field degree: | $24576$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
16.96.0-16.e.1.8 | $16$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.96.0-16.e.1.8 | $16$ | $5$ | $5$ | $0$ | $0$ |
40.240.8-40.z.1.7 | $40$ | $2$ | $2$ | $8$ | $2$ |
80.240.8-80.q.1.16 | $80$ | $2$ | $2$ | $8$ | $?$ |
80.240.8-80.q.1.19 | $80$ | $2$ | $2$ | $8$ | $?$ |
80.240.8-80.q.2.5 | $80$ | $2$ | $2$ | $8$ | $?$ |
80.240.8-80.q.2.32 | $80$ | $2$ | $2$ | $8$ | $?$ |
80.240.8-40.z.1.4 | $80$ | $2$ | $2$ | $8$ | $?$ |