Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $64$ | ||
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 $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}7&56\\60&67\end{bmatrix}$, $\begin{bmatrix}13&40\\60&9\end{bmatrix}$, $\begin{bmatrix}17&40\\5&39\end{bmatrix}$, $\begin{bmatrix}19&16\\21&1\end{bmatrix}$, $\begin{bmatrix}23&72\\62&51\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 16.48.1.g.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: | 64.2.a.a |
Models
Weierstrass model Weierstrass model
$ y^{2} $ | $=$ | $ x^{3} + x $ |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Maps to other modular curves
$j$-invariant map of degree 48 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
$\displaystyle j$ | $=$ | $\displaystyle 2^2\,\frac{12490x^{2}y^{12}z^{2}-15913131x^{2}y^{8}z^{6}+113246025x^{2}y^{4}z^{10}-16777215x^{2}z^{14}-188xy^{14}z+3354639xy^{10}z^{5}-104857784xy^{6}z^{9}+83886081xy^{2}z^{13}+y^{16}-335468y^{12}z^{4}+41954972y^{8}z^{8}-67109046y^{4}z^{12}+z^{16}}{zy^{4}(x^{2}y^{8}z-x^{2}y^{4}z^{5}-x^{2}z^{9}-xy^{10}-xy^{2}z^{8}+2y^{8}z^{3}-2y^{4}z^{7}-z^{11})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.48.0-8.q.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.48.0-16.h.1.2 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-16.h.1.16 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.0-8.q.1.1 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
80.48.1-16.a.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
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 |
---|---|---|---|---|---|---|
80.192.1-16.l.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-16.l.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-16.n.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-16.n.2.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bh.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bh.2.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bl.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.1-80.bl.2.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
80.192.3-16.cn.1.3 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-16.co.1.2 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-16.cp.1.2 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-16.cp.2.2 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.gy.1.3 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.gz.1.5 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.ha.1.1 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.192.3-80.ha.2.1 | $80$ | $2$ | $2$ | $3$ | $?$ | not computed |
80.480.17-80.m.1.21 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.1-48.bh.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-48.bh.2.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-48.bl.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-48.bl.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dx.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dx.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ef.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ef.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-48.fw.1.3 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-48.fx.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-48.fy.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-48.fy.2.4 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sa.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sb.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sc.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sc.2.3 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-48.y.1.7 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-48.mg.1.37 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |