Embedded model Embedded model in $\mathbb{P}^{3}$
| $ 0 $ | $=$ | $ 4 x^{2} + 8 x y + 2 x z - 3 y^{2} + 2 y z + 2 z^{2} $ |
| $=$ | $11 x^{2} - 6 x y + 2 x z - 10 y^{2} + 2 y z + 2 z^{2} - 2 w^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 4 x^{4} + 16 x^{3} y + 76 x^{2} y^{2} + 42 x^{2} z^{2} + 8 x y^{3} - 112 x y z^{2} - 223 y^{4} + \cdots + 196 z^{4} $ |
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This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps between models of this curve
Birational map from embedded model to plane model:
| $\displaystyle X$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{2}{7}w$ |
Maps to other modular curves
$j$-invariant map
of degree 96 from the embedded model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^3}{7^4}\cdot\frac{7109684297088306355931353647391105673457308768883118080xz^{23}+40494060072015965775368334156973975883952195630374922240xz^{21}w^{2}+79711172506390381380232370636205890748436441147481545728xz^{19}w^{4}+61895253010331528694599659833458830536167515180120624640xz^{17}w^{6}+16445546319193042031177470763927602667970919620692529664xz^{15}w^{8}+6963567853959701536769977465265745562068299186157614336xz^{13}w^{10}+1247105882115057112475292123916597723134917075995803008xz^{11}w^{12}-2395276974879494896849144669911596606173366849200606016xz^{9}w^{14}-952547184360896945936731237744897938060388542338926128xz^{7}w^{16}-488122533582996664125505233690553731404463158490268792xz^{5}w^{18}-58289801785812829906691106467576779829191470306627764xz^{3}w^{20}-3237233200844404057275808540885961509701004048939930xzw^{22}-47199861281333848708181747271821095968231588027160688640y^{2}z^{22}-238695342843149650698134307234593814247488539207129902080y^{2}z^{20}w^{2}-375462486061397543710916613552799003295802587338928558592y^{2}z^{18}w^{4}-158541244273463127962646272718079886835626262689471179008y^{2}z^{16}w^{6}-4315924539656316605639697047543111245706463492509120256y^{2}z^{14}w^{8}-61113761716108848930862518503445271192239087286697827712y^{2}z^{12}w^{10}+6284444659870655634222742846644914015577103936675649216y^{2}z^{10}w^{12}-12814087854023872179380728665841132694047932636984993696y^{2}z^{8}w^{14}-1799790358787468188391939511309380498104618537869551640y^{2}z^{6}w^{16}-838978909414801154092290295791344846353702179038562300y^{2}z^{4}w^{18}-48410950352614273218403010159802430948495996469544858y^{2}z^{2}w^{20}-939723565334432683325314555765058575483179765162845y^{2}w^{22}-25289945194414120421404165982202417006586180357020119040yz^{23}-122413784717735176977035595716287006613192882750269544448yz^{21}w^{2}-176222699984163911349666116319457900521352065597176030208yz^{19}w^{4}-50125947263944873649966649434101194580698826766316728832yz^{17}w^{6}+9252490993488451694367227494983612483907921472477073920yz^{15}w^{8}-28927646611387477232197787780997357759079116098546494208yz^{13}w^{10}+21605129962266637568260140301259955625912005315301469568yz^{11}w^{12}+1140291381349764592609888679518772232852437459931131072yz^{9}w^{14}+3755777111249967874444917658963508242021910564194870224yz^{7}w^{16}+351945597335655592537015515787530299788556235066567816yz^{5}w^{18}+80036501797645724566056838951673010550113447897553100yz^{3}w^{20}+1240223355101394245559636794206369699676111195221030yzw^{22}-2307916608106378947062463292732586844241803459028365312z^{24}-11624932821214693155769628879640100739515795967743236096z^{22}w^{2}-20314121713225937319442429564523946276718191688982946816z^{20}w^{4}-16808601824266641944043896472928469844130661112418787840z^{18}w^{6}-14770992240061972440760514126774152415994176594088258048z^{16}w^{8}-14864496819491895226294037614379020077732055224812483328z^{14}w^{10}-5847037679889887126228039249259004042362152915018207872z^{12}w^{12}-4373094534540716490037133850707754385024013042697468224z^{10}w^{14}-1468232145244844929423127814501293670747377807969060208z^{8}w^{16}-576734933610095626922953349494178931802817245606099640z^{6}w^{18}-100190861688886415052468479847850096012140134280356340z^{4}w^{20}-9044772540089881997390900236223228311713028456964490z^{2}w^{22}-174189951999914896787724930168850006702707222381396w^{24}}{13708956717664527041069603805881626624433701946880xz^{23}-32317469626535142255437903108607521721520670886912xz^{21}w^{2}+20455002770208989169416272624053480829804490169088xz^{19}w^{4}+9517394412879658000240366404527184583957457628288xz^{17}w^{6}-16571090529118638351174158178501722441842034540672xz^{15}w^{8}+3077320537951422376364726258431506470306316646944xz^{13}w^{10}+2979144714989499789437526610897611933028585647696xz^{11}w^{12}-656561186641294555299896235169250537515041445544xz^{9}w^{14}-221937806862221515926912421295445032984876962654xz^{7}w^{16}+6777964703655311071265138488161584853042511266xz^{5}w^{18}+5483122205936770432062780814625217331773033528xz^{3}w^{20}+1488839789152682240192713690556796077287649760xzw^{22}-91011193795281766679357650500218072655358855159040y^{2}z^{22}+287963120453550067124187197339355516179498100756992y^{2}z^{20}w^{2}-350515258022166722774738378672530233829825619827328y^{2}z^{18}w^{4}+181393588535476910612452614429214422701400200499776y^{2}z^{16}w^{6}-3752065792715247309796475449861912488622649116736y^{2}z^{14}w^{8}-33362484642933762479160516435075490957518581003504y^{2}z^{12}w^{10}+6695279647285427982045428016589899993817482143016y^{2}z^{10}w^{12}+2685960164632919037711505649365455297266438453996y^{2}z^{8}w^{14}-425188499704321180258131464257853900765222285007y^{2}z^{6}w^{16}-138064390992124982703003246546648628892802204679y^{2}z^{4}w^{18}+7424695480193933940484426901411274138416968356y^{2}z^{2}w^{20}+806923102605599283487081248052519714152004176y^{2}w^{22}-48764298044052093304881002480066980206137451133440yz^{23}+166087513351028505023915967371490123919018167325696yz^{21}w^{2}-223859636482101696282527586636168069458815835342080yz^{19}w^{4}+138784009031967184555638988249173607861151588113536yz^{17}w^{6}-22880015940877920389020027235111339982011431751808yz^{15}w^{8}-18163851706643997681670723242893561984362961929696yz^{13}w^{10}+8313542301923163574632528756665567898745930958928yz^{11}w^{12}+772088729633049265377157511876022450765991762520yz^{9}w^{14}-727581635843472024345901485410269286443288359198yz^{7}w^{16}-34769384794798062787614858310006673822531554686yz^{5}w^{18}+21245924204004529069412370573993772425924184248yz^{3}w^{20}+1369975701188908334780789113966871411029405152yzw^{22}-4450145402583759365431192428950489079090894725632z^{24}+14482245219217535934777816332852703708515404913664z^{22}w^{2}-19389452742799258065778750289006416386978318791936z^{20}w^{4}+12632700561623465496234981686912217835649163518080z^{18}w^{6}-3896449601015060662576297177756662700489972016512z^{16}w^{8}-98924679626782079818686137593464255759026563040z^{14}w^{10}+1013907677611813886037803589378142173115437034576z^{12}w^{12}-326195329078624525303494805805528132475495637736z^{10}w^{14}-108080448403531678209174153662980462180066428006z^{8}w^{16}+31150071040982517988359783061320070407449141978z^{6}w^{18}+2147098222634358222158286297959610054472167704z^{4}w^{20}+1189354507140171095505758478444599849877651024z^{2}w^{22}-233893507952650518036623642849386692963865344w^{24}}$ 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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.
