Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 396x - 3024 $ |
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This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.
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}\cdot\frac{42708539224x^{2}y^{30}+723164799037248x^{2}y^{29}z+1819963413419811840x^{2}y^{28}z^{2}+1186127859982777445376x^{2}y^{27}z^{3}-224212009488688998383616x^{2}y^{26}z^{4}-629800351233912554938675200x^{2}y^{25}z^{5}-325776851369113892399362934784x^{2}y^{24}z^{6}-53607397228083171760322465759232x^{2}y^{23}z^{7}+27616661699472782159193723787739136x^{2}y^{22}z^{8}+24053394879767433706904468938893557760x^{2}y^{21}z^{9}+10209422557140714742669397154268966748160x^{2}y^{20}z^{10}+3111981814739515219219888381521235959349248x^{2}y^{19}z^{11}+754324712181584338136648750072451313724030976x^{2}y^{18}z^{12}+152313480795306211398060495757336180393909420032x^{2}y^{17}z^{13}+26304330166621580039770657095950065679841940733952x^{2}y^{16}z^{14}+3950607059590056578612516273606738045460925875486720x^{2}y^{15}z^{15}+521740325614053361173288478801282984047725886817959936x^{2}y^{14}z^{16}+61038567278621176490390800676015966742407172904609382400x^{2}y^{13}z^{17}+6355430088421635906818404622452120130692184163067858255872x^{2}y^{12}z^{18}+590413347096220590979254366060594497112611146923234293710848x^{2}y^{11}z^{19}+48962913104537650350621657187253123738215050554835688539291648x^{2}y^{10}z^{20}+3619665174447123080963409465817457911793675796506947110146408448x^{2}y^{9}z^{21}+237705377118754364968677621150764296733880291042586968607791513600x^{2}y^{8}z^{22}+13784023707942243908507465402040449952026349542837883814265562857472x^{2}y^{7}z^{23}+699321055272772267621437129179581864507221237882128995134869593915392x^{2}y^{6}z^{24}+30617888882110457437076691092649109267387528553905440487500281177702400x^{2}y^{5}z^{25}+1133220460869093289104210425561063854664977463812876375144824439597694976x^{2}y^{4}z^{26}+34333414335363460372299035185222125468819506894725123902717923379747225600x^{2}y^{3}z^{27}+806609586707857338974961318342325349845063558155571609698397186682429374464x^{2}y^{2}z^{28}+13233895499344253150571171954893471962979237470986970396820494283228986736640x^{2}yz^{29}+115649302594597702047661550014343055413119538942885477584090479580810397614080x^{2}z^{30}+798916552xy^{31}+36898243626672xy^{30}z+156775535156256768xy^{29}z^{2}+162244384283597241600xy^{28}z^{3}+20429339603912274493440xy^{27}z^{4}-60830875503595302543134208xy^{26}z^{5}-45518041991679637774986362880xy^{25}z^{6}-12877064975648941799061886230528xy^{24}z^{7}+1256957172027541170763537486381056xy^{23}z^{8}+2825612791297300211876439558308757504xy^{22}z^{9}+1463483236784256924556925718443549786112xy^{21}z^{10}+503833141445454268756669901205137766481920xy^{20}z^{11}+134406781218744769580862182188928930257305600xy^{19}z^{12}+29513843739645541656087730549917849199001468928xy^{18}z^{13}+5508675735786509171043772739273684244983426580480xy^{17}z^{14}+891330220704577856732708358350183740535987792510976xy^{16}z^{15}+126658688127391065794228595834781026409743570752765952xy^{15}z^{16}+15945923141148864108458766867557515191417550977802174464xy^{14}z^{17}+1789060601716445196521713420332606264018785266968242946048xy^{13}z^{18}+179525372725951898350175441950198791595487501401181141336064xy^{12}z^{19}+16139544890646263665600392367600228664453402997143332768972800xy^{11}z^{20}+1299858146866287811217210034878398297628826665637768177433706496xy^{10}z^{21}+93613269820177975052996938449980107484038179311417548163694723072xy^{9}z^{22}+6005508249399724103702984473026978022068554732066081028323596566528xy^{8}z^{23}+341054219303328563988161667756558547864431567310261310225052157870080xy^{7}z^{24}+16985706437339933754262135047297409298315357163029811830963904335314944xy^{6}z^{25}+731690747812175576404974506960520934367852852011513218114627674755301376xy^{5}z^{26}+26705516257196482754996489682959984046500234729498387392849204016628891648xy^{4}z^{27}+799807436891964644499323306118505483906110628439898936390971235761186144256xy^{3}z^{28}+18625710938351672534379202973601234993549748644685820179022506409506998583296xy^{2}z^{29}+303990026974476388496986299590657173421127123525843663326177926012200107900928xyz^{30}+2656529562066826696668979265548357223982192951030068289621221555186171149025280xz^{31}+7189057y^{32}+1470767441184y^{31}z+11582612934155136y^{30}z^{2}+18282284644442969088y^{29}z^{3}+6535963351784888547840y^{28}z^{4}-5029841399088658678382592y^{27}z^{5}-5559819848039561504688082944y^{26}z^{6}-2052704836594822227023592603648y^{25}z^{7}-64809554070317374497623635869696y^{24}z^{8}+307823786446118562811934029184237568y^{23}z^{9}+185688675421550130916638567645959946240y^{22}z^{10}+68265729599930419595013215117238037118976y^{21}z^{11}+18931125023069542261334116194909614029406208y^{20}z^{12}+4264882498242206095414651479827701217252868096y^{19}z^{13}+810376190171080286614462631224798277379286892544y^{18}z^{14}+132829112445225225705806080987293249997362954240000y^{17}z^{15}+19060520170644317050194772962392071365345773610860544y^{16}z^{16}+2418741820635319677733643118703682512892755128518443008y^{15}z^{17}+273318549884516079328907839700820950757713330796748603392y^{14}z^{18}+27629652858386771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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.
