Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}9&64\\45&59\end{bmatrix}$, $\begin{bmatrix}21&24\\17&71\end{bmatrix}$, $\begin{bmatrix}25&32\\3&67\end{bmatrix}$, $\begin{bmatrix}57&48\\74&5\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.96.1.bf.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $96$ |
Full 80-torsion field degree: | $61440$ |
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 |
---|---|---|---|---|---|---|
16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-40.bf.2.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.96.0-16.j.1.5 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-40.bf.2.8 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bs.2.6 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bs.2.9 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bt.2.6 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bt.2.9 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.1-80.g.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.g.1.6 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.bq.2.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.bq.2.9 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.br.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.br.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
80.384.5-80.lk.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
80.384.5-80.ll.1.3 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
80.384.5-80.lo.2.3 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
80.384.5-80.lp.2.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.bt.1.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.bu.1.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.ck.1.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.cn.1.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.ea.1.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.ed.1.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.et.1.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.eu.1.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bqv.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bqx.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.brf.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.brh.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |