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: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
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: | 16M1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}7&16\\47&49\end{bmatrix}$, $\begin{bmatrix}9&0\\54&1\end{bmatrix}$, $\begin{bmatrix}47&56\\23&13\end{bmatrix}$, $\begin{bmatrix}67&16\\35&57\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.96.1.bg.2 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 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 |
---|---|---|---|---|---|---|
16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-40.bf.2.5 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.96.0-16.j.1.7 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-40.bf.2.5 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bk.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bk.1.13 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bl.1.2 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.0-80.bl.1.7 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.96.1-80.h.1.10 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.h.1.19 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.by.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.by.2.13 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.bz.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.bz.1.13 | $80$ | $2$ | $2$ | $1$ | $?$ | 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.lm.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
80.384.5-80.ln.1.2 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
80.384.5-80.lq.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.bs.1.7 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.bv.2.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.cl.1.7 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.cm.2.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.eb.2.1 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.ec.2.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.es.2.1 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
160.384.5-160.ev.2.3 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bqw.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bqy.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.brg.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.brj.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |