Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $32$ | ||
| 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: | 16G1 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}23&6\\36&21\end{bmatrix}$, $\begin{bmatrix}31&68\\70&17\end{bmatrix}$, $\begin{bmatrix}35&46\\24&45\end{bmatrix}$, $\begin{bmatrix}46&39\\41&72\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 16.48.1.u.2 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: | 32.2.a.a |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 11x - 14 $ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{696x^{2}y^{14}-43760146x^{2}y^{12}z^{2}-3169749624x^{2}y^{10}z^{4}+897758511351x^{2}y^{8}z^{6}+1883896278384x^{2}y^{6}z^{8}-6414136372283289x^{2}y^{4}z^{10}-273771076691950884x^{2}y^{2}z^{12}-3203095830928031745x^{2}z^{14}-162316xy^{14}z-86431272xy^{12}z^{3}+830898561xy^{10}z^{5}+4358313903318xy^{8}z^{7}-118577637265816xy^{6}z^{9}-31833116481580536xy^{4}z^{11}-1145262787644097977xy^{2}z^{13}-12262818962286313470xz^{15}-y^{16}+12870768y^{14}z^{2}-1154513508y^{12}z^{4}+135555226296y^{10}z^{6}+8271357474868y^{8}z^{8}-1145847995474016y^{6}z^{10}-82121544224773674y^{4}z^{12}-1745005629946205184y^{2}z^{14}-11713254600860499961z^{16}}{y^{2}(x^{2}y^{12}+17876x^{2}y^{10}z^{2}+14822642x^{2}y^{8}z^{4}+2688555872x^{2}y^{6}z^{6}+155306688875x^{2}y^{4}z^{8}+2710594125844x^{2}y^{2}z^{10}+x^{2}z^{12}+48xy^{12}z+213038xy^{10}z^{3}+104584100xy^{8}z^{5}+14134791018xy^{6}z^{7}+676792892740xy^{4}z^{9}+10377312075737xy^{2}z^{11}-2xz^{13}+1136y^{12}z^{2}+1879472y^{10}z^{4}+510661199y^{8}z^{6}+41741662168y^{6}z^{8}+1197423457708y^{4}z^{10}+9912247648112y^{2}z^{12}-7z^{14})}$ |
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.ba.2.8 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 80.48.0-16.e.2.3 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.0-16.e.2.9 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.0-8.ba.2.6 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.1-16.b.1.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.48.1-16.b.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.d.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-16.i.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-16.m.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-16.r.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.cm.1.6 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.cq.1.5 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.dc.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.dg.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.480.17-80.ce.1.5 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
| 160.192.5-32.r.2.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-32.v.2.6 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-32.z.2.7 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-32.bd.2.7 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-160.bt.2.2 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-160.bx.1.1 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-160.cr.1.8 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 160.192.5-160.cv.1.7 | $160$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.192.1-48.cn.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-48.cr.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-48.dd.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-48.dh.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.jl.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.jt.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.kr.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.kz.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.288.9-48.ey.1.5 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 240.384.9-48.baz.2.10 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |