Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}25&32\\61&69\end{bmatrix}$, $\begin{bmatrix}37&48\\49&19\end{bmatrix}$, $\begin{bmatrix}39&24\\75&17\end{bmatrix}$, $\begin{bmatrix}75&56\\46&73\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.1.f.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $192$ |
Full 80-torsion field degree: | $122880$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
16.48.0-8.k.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.48.0-8.k.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.48.0-80.p.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-80.p.1.29 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.1-80.b.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.48.1-80.b.1.27 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
80.192.1-80.y.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.y.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.z.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.z.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.ba.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.ba.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bb.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bb.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.480.17-80.j.1.9 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.1-240.dc.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dc.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dd.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dd.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.de.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.de.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.df.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.df.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.x.1.3 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.bwt.1.33 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |