Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 9x $ |
![Copy content]()
![Toggle raw display]()
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{2^2}{3^4}\cdot\frac{177058726x^{2}y^{30}+9686203880x^{2}y^{29}z-803359521533x^{2}y^{28}z^{2}-83681102739240x^{2}y^{27}z^{3}-1566486007306416x^{2}y^{26}z^{4}+56178047554957800x^{2}y^{25}z^{5}+407440478881900836x^{2}y^{24}z^{6}-268102978207033743612x^{2}y^{22}z^{8}+4269442406966852360400x^{2}y^{21}z^{9}-57457633415643657162999x^{2}y^{20}z^{10}+772983302830283236813020x^{2}y^{19}z^{11}-6364703494223432750490966x^{2}y^{18}z^{12}+6403164488712496933273980x^{2}y^{17}z^{13}+491464752799210938154623915x^{2}y^{16}z^{14}-6212053450221547040101454400x^{2}y^{15}z^{15}+37920346726145384599344707706x^{2}y^{14}z^{16}-78286761629511318134792368200x^{2}y^{13}z^{17}-708142181763011853353152968999x^{2}y^{12}z^{18}+7453473343352944943434038490680x^{2}y^{11}z^{19}-32200733100773401577859777230664x^{2}y^{10}z^{20}+48821869713850905247825608576180x^{2}y^{9}z^{21}+222371943525726534372412210691340x^{2}y^{8}z^{22}-1607286862053492119112614141995200x^{2}y^{7}z^{23}+4719834410465624717904869997752778x^{2}y^{6}z^{24}-6636832143979708138256450644984920x^{2}y^{5}z^{25}-2203154471280103491218814706322178x^{2}y^{4}z^{26}+32970380793060962414062225910452140x^{2}y^{3}z^{27}-81258693302410581033217577408439402x^{2}y^{2}z^{28}+104772627903303758053138306958357580x^{2}yz^{29}-57845045566138338169254042378696495x^{2}z^{30}-12683020xy^{31}+4104226369xy^{30}z+600684861380xy^{29}z^{2}+18791172205272xy^{28}z^{3}-121122951311520xy^{27}z^{4}-18358229498950782xy^{26}z^{5}-292965943211124840xy^{25}z^{6}+9367141248009215928xy^{24}z^{7}-65170786279071525480xy^{23}z^{8}+1244193882954222584106xy^{22}z^{9}-25029098814378415025160xy^{21}z^{10}+178076921430859671700026xy^{20}z^{11}+1025533100618074085812020xy^{19}z^{12}-37120784467698833492537595xy^{18}z^{13}+449689404846282377818580280xy^{17}z^{14}-3076765958181069607766211144xy^{16}z^{15}+6986452549862058508431833580xy^{15}z^{16}+89657012421651600690157533699xy^{14}z^{17}-1085914169956452383206315772580xy^{13}z^{18}+5476293038356742997753980220864xy^{12}z^{19}-9150398994857159428496625620880xy^{11}z^{20}-58895612647683457805255893459527xy^{10}z^{21}+485120166612115255648847234172180xy^{9}z^{22}-1668847934598147358815742013173212xy^{8}z^{23}+2399627440786747926865290767626140xy^{7}z^{24}+4715862874111924526617263757324125xy^{6}z^{25}-34802050273153299295680282600430260xy^{5}z^{26}+90287460681506753833316477431486566xy^{4}z^{27}-122234716594577267745658380693041940xy^{3}z^{28}+70699504733502766864008743576200329xy^{2}z^{29}+389017y^{32}-1293134380y^{31}z-148983078968y^{30}z^{2}-2319324197760y^{29}z^{3}+243044638275348y^{28}z^{4}+5338036867831920y^{27}z^{5}-33368876413437492y^{26}z^{6}-1739596254491303640y^{25}z^{7}-10635205134463814520y^{24}z^{8}+470570044392615408120y^{23}z^{9}-738712202330287318464y^{22}z^{10}-75962174815746444911220y^{21}z^{11}+1471682698009239286324233y^{20}z^{12}-17495509013052172149024540y^{19}z^{13}+129969552797652144434030262y^{18}z^{14}-297423122952482192768949540y^{17}z^{15}-5075965208491394793505285896y^{16}z^{16}+64606792354012867614319927980y^{15}z^{17}-348852917068195773279563464536y^{14}z^{18}+614562898362335792025157727280y^{13}z^{19}+4407890067603604197657476660808y^{12}z^{20}-38246784142601926238088415770720y^{11}z^{21}+138167058584967843045466712053206y^{10}z^{22}-199770627504835181245077977844060y^{9}z^{23}-487969420532068919725393298647752y^{8}z^{24}+3459845436173759937541596341798700y^{7}z^{25}-9028765344288493024729360977935664y^{6}z^{26}+12288135172114695031070582270681460y^{5}z^{27}-7141313582065985454619885353665169y^{4}z^{28}+141493456670804973088067505420y^{3}z^{29}+174362281342500822973199169606y^{2}z^{30}+112408821430315064449689425580yz^{31}+31030502386435713169515106137z^{32}}{164x^{2}y^{30}-13127935x^{2}y^{28}z^{2}+6388120388x^{2}y^{26}z^{4}-3496261945581x^{2}y^{24}z^{6}-1390975188362784x^{2}y^{22}z^{8}+309959157854102697x^{2}y^{20}z^{10}-17312725592528003280x^{2}y^{18}z^{12}-153051884409010783680x^{2}y^{16}z^{14}+50787017040979168064676x^{2}y^{14}z^{16}-2161589234124081312400635x^{2}y^{12}z^{18}+43591925322299593814147100x^{2}y^{10}z^{20}-441315462255847727264783010x^{2}y^{8}z^{22}+1585109251630546427644375104x^{2}y^{6}z^{24}+7578101959415318425334744709x^{2}y^{4}z^{26}-75265568676888227973851357628x^{2}y^{2}z^{28}+148695418365105736174136457735x^{2}z^{30}-11902xy^{30}z+216456344xy^{28}z^{3}+77840040047xy^{26}z^{5}+36479359074024xy^{24}z^{7}-7915012087483548xy^{22}z^{9}-366352278730763076xy^{20}z^{11}+135499950196589271330xy^{18}z^{13}-9918585187810184432520xy^{16}z^{15}+334420969432846869533106xy^{14}z^{17}-5222152725904882507417560xy^{12}z^{19}+9184525586379922239787014xy^{10}z^{21}+931242023934727266123783804xy^{8}z^{23}-14037226347579362662367709450xy^{6}z^{25}+83628431573415408109645509924xy^{4}z^{27}-181738856485713392638390465137xy^{2}z^{29}-y^{32}+499412y^{30}z^{2}-2117342710y^{28}z^{4}-505866907080y^{26}z^{6}+136275845806422y^{24}z^{8}+32547331172689416y^{22}z^{10}-7481703183692918148y^{20}z^{12}+529682330616310479780y^{18}z^{14}-16934658981409792244070y^{16}z^{16}+197565917923389692705148y^{14}z^{18}+2633878283686928906772258y^{12}z^{20}-112837345687786339081844748y^{10}z^{22}+1443444550651746384236365797y^{8}z^{24}-8362765340417643957057470652y^{6}z^{26}+18357313919210211034450203012y^{4}z^{28}+161502427958112242192484y^{2}z^{30}-79766443076872509863361z^{32}}$ |
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.
