Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}3&46\\4&37\end{bmatrix}$, $\begin{bmatrix}66&53\\41&10\end{bmatrix}$, $\begin{bmatrix}67&10\\76&57\end{bmatrix}$, $\begin{bmatrix}74&31\\71&62\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.24.1.d.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $24$ |
Cyclic 80-torsion field degree: | $768$ |
Full 80-torsion field degree: | $245760$ |
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 |
---|---|---|---|---|---|---|
16.24.0-8.o.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.24.0-8.o.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
80.96.1-80.b.1.15 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.e.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.n.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.p.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.co.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.cr.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.cs.1.6 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.96.1-80.cv.1.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.240.9-80.h.1.14 | $80$ | $5$ | $5$ | $9$ | $?$ | not computed |
80.288.9-80.p.1.23 | $80$ | $6$ | $6$ | $9$ | $?$ | not computed |
80.480.17-80.dl.1.23 | $80$ | $10$ | $10$ | $17$ | $?$ | not computed |
240.96.1-240.bz.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.cb.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.cd.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.cf.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hn.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hp.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hr.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ht.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.144.5-240.d.1.54 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
240.192.5-240.bvy.1.48 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |