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: | $\begin{bmatrix}11&56\\22&31\end{bmatrix}$, $\begin{bmatrix}31&72\\34&59\end{bmatrix}$, $\begin{bmatrix}69&48\\47&17\end{bmatrix}$, $\begin{bmatrix}75&16\\26&13\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.1.q.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 |
---|---|---|---|---|---|---|
16.48.1-16.a.1.14 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
40.48.0-40.bj.1.12 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.48.0-80.p.1.10 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-80.p.1.19 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-40.bj.1.7 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.1-16.a.1.15 | $80$ | $2$ | $2$ | $1$ | $?$ | 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.ce.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.ce.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.cf.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.cf.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.cg.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.cg.2.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.ch.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.ch.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.480.17-80.bg.1.9 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.1-240.hp.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hp.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hq.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hq.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hr.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hr.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hs.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.hs.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.cu.1.17 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.ein.1.33 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |