Embedded model Embedded model in $\mathbb{P}^{7}$
| $ 0 $ | $=$ | $ z v + w r $ |
| $=$ | $x r + y v$ |
| $=$ | $x z - y w$ |
| $=$ | $x z - x r - y t + z u$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 375 x^{8} y^{2} z^{2} - 125 x^{8} z^{4} - 6300 x^{6} y^{4} z^{2} - 9150 x^{6} y^{2} z^{4} + \cdots - 75625 z^{12} $ |
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This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Maps between models of this curve
Birational map from embedded model to plane model:
| $\displaystyle X$ |
$=$ |
$\displaystyle r$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{5}u$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{5}v$ |
Maps to other modular curves
$j$-invariant map
of degree 120 from the embedded model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -\frac{2^{12}}{11^4}\cdot\frac{213228736672497204988153500xur^{8}+112235054834460622561200zu^{8}r-6834387968024854877640000zu^{6}r^{3}+90683315663928189675264000zu^{4}r^{5}-415636541436282291262080000zu^{2}r^{7}+435509725863584533708800000zr^{9}-79780243342897222413750wv^{9}-4501242260344614471008850wv^{7}r^{2}-69491307707509932044806500wv^{5}r^{4}-376836720496743105724577750wv^{3}r^{6}+228644364727711462717522500wvr^{8}+35666064202364383963725tv^{9}+5074299704505450181455000tv^{7}r^{2}+43281471629464592081184000tv^{5}r^{4}+25355676049810127543583125tv^{3}r^{6}-117947334003777623898482500tvr^{8}+1231936277850356404293u^{10}-335709636897192219416700u^{8}r^{2}+6641360508541861044360000u^{6}r^{4}-32237321607120335334552000u^{4}r^{6}-47805607782801589750425u^{2}v^{8}+5303160244560124349223975u^{2}v^{6}r^{2}+50006715022067220823267125u^{2}v^{4}r^{4}-23973392910946388681863500u^{2}v^{2}r^{6}+2603355733326297492864000u^{2}r^{8}-16152107301522551781675v^{10}+1616893013223051387456600v^{8}r^{2}+7411727663218721925460125v^{6}r^{4}-43144040926591572464796625v^{4}r^{6}+133244656097300989437770000v^{2}r^{8}-139407722747626291200000r^{10}}{5480309976402279367500xur^{8}+1002488063082184800zu^{8}r+74103274905919776000zu^{6}r^{3}-798015589966324224000zu^{4}r^{5}+2614318698586682880000zu^{2}r^{7}-1849544837408688750wv^{9}-70083999530680919850wv^{7}r^{2}-1020114999926007826500wv^{5}r^{4}-6050518723048948958750wv^{3}r^{6}-6257899325417943967500wvr^{8}+1559607918625278225tv^{9}+75240437319907695000tv^{7}r^{2}+643711204799742024000tv^{5}r^{4}+286033534055384455625tv^{3}r^{6}-7015177808385479612500tvr^{8}+454878958623541353u^{10}-3679586867903928300u^{8}r^{2}+130160600664539148000u^{6}r^{4}-1142242712789629968000u^{4}r^{6}+1080452442783921075u^{2}v^{8}+89335064411036237475u^{2}v^{6}r^{2}+915793408416995249625u^{2}v^{4}r^{4}+1051488370653812152500u^{2}v^{2}r^{6}+2614318698586682880000u^{2}r^{8}+332957895831264825v^{10}+25563815471874972600v^{8}r^{2}+195191684198231972625v^{6}r^{4}+152675976521648166875v^{4}r^{6}+4316968250055825530000v^{2}r^{8}}$ |
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Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.
