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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}5&56\\66&65\end{bmatrix}$, $\begin{bmatrix}33&8\\76&17\end{bmatrix}$, $\begin{bmatrix}33&60\\4&31\end{bmatrix}$, $\begin{bmatrix}37&24\\54&37\end{bmatrix}$, $\begin{bmatrix}73&4\\62&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.1.a.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $384$ |
Full 80-torsion field degree: | $122880$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.48.0-8.i.1.8 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-80.r.1.5 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-80.r.1.12 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.1-80.c.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.48.1-80.c.1.12 | $80$ | $2$ | $2$ | $1$ | $?$ | 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.e.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.e.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.n.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.n.2.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.3-80.cb.2.1 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.cd.1.3 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.cd.2.10 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.cg.1.12 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.cg.2.4 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.ch.1.3 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.de.2.5 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.dh.1.10 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.dh.2.2 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.dj.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.dj.2.5 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.dk.2.1 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.480.17-80.b.2.12 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.1-240.h.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.h.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bl.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bl.2.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-240.fs.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fu.1.23 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fu.2.2 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fw.1.22 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fw.2.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ga.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.in.1.3 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.is.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.is.2.18 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iu.1.18 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iu.2.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iy.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-240.a.2.39 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.bsb.2.23 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |