Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 9x $ |
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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 to other modular curves
$j$-invariant map
of degree 72 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^6}{3^{12}}\cdot\frac{428813569200x^{2}y^{46}+594931748757792x^{2}y^{45}z+139935842468334126x^{2}y^{44}z^{2}+11686730482932916224x^{2}y^{43}z^{3}+461557541549239109088x^{2}y^{42}z^{4}+9625770780420958458480x^{2}y^{41}z^{5}+105603894126448891548303x^{2}y^{40}z^{6}+841267375103034626500608x^{2}y^{39}z^{7}+40489356897021678635180592x^{2}y^{38}z^{8}+2517521104725776595985935456x^{2}y^{37}z^{9}+104072716955450277970117807878x^{2}y^{36}z^{10}+2849549960338762701433189957632x^{2}y^{35}z^{11}+37516591037607523973832949425504x^{2}y^{34}z^{12}-763586080134503431743956925525024x^{2}y^{33}z^{13}-60425936040535836761261567969254458x^{2}y^{32}z^{14}-1941640942387978608464651195994181632x^{2}y^{31}z^{15}-42053152040447314499645564543342566464x^{2}y^{30}z^{16}-677525824399272702166177430931463743360x^{2}y^{29}z^{17}-8373417419149245151384873765269533472072x^{2}y^{28}z^{18}-79116071071840319610751878685904320512000x^{2}y^{27}z^{19}-541422456576028948363691042736489253196928x^{2}y^{26}z^{20}-2070025506195193539004492177273917013160592x^{2}y^{25}z^{21}+6538833729629980885778349721630237656815367x^{2}y^{24}z^{22}+196856596956586893893134365594407282951841792x^{2}y^{23}z^{23}+2010627702001494284762715761116970729807733360x^{2}y^{22}z^{24}+14122983068800315643958295556254024693956587616x^{2}y^{21}z^{25}+75273035948904493836013257050047736625567791370x^{2}y^{20}z^{26}+304736617472974186283465257655745666636577554432x^{2}y^{19}z^{27}+849343019674753135144751080727789827988365974816x^{2}y^{18}z^{28}+764856773655164972559976604400260291956728429792x^{2}y^{17}z^{29}-7990243298939307294337730458379116872498816354570x^{2}y^{16}z^{30}-61232603875983164650611417816927013387155315634176x^{2}y^{15}z^{31}-271006853266337718068337123562396335943321031444496x^{2}y^{14}z^{32}-889142499813371957188179872716278235259552310389856x^{2}y^{13}z^{33}-2270595898644293185368447621201671350973424696995034x^{2}y^{12}z^{34}-4446632591824668458644935296997247212120616988123136x^{2}y^{11}z^{35}-6006152544799842665698138456620450566230369481243808x^{2}y^{10}z^{36}-2642577286571135933135807538299049818662815158993328x^{2}y^{9}z^{37}+12810821955087785335617320080112700735064771552751565x^{2}y^{8}z^{38}+46267032031182232751929374466609719565649213949523968x^{2}y^{7}z^{39}+94416701502702370737650634008561109715989576590604816x^{2}y^{6}z^{40}+139540130375404424991730061439918200754691766910376224x^{2}y^{5}z^{41}+156546919520858609762126629019737118194753474303095525x^{2}y^{4}z^{42}+132256157103504519229481343205993923735424523369484288x^{2}y^{3}z^{43}+80159259436699638309243044087513936838284512242934320x^{2}y^{2}z^{44}+31187313994490687296935670400687671773542545996702800x^{2}yz^{45}+5844613855896621038372971357819017094221846482977125x^{2}z^{46}+18594510000xy^{47}+69037180812948xy^{46}z+25998339092281344xy^{45}z^{2}+2919944805731206368xy^{44}z^{3}+143614984701527831712xy^{43}z^{4}+3590125609853377509381xy^{42}z^{5}+44981563635821995026432xy^{41}z^{6}+184664359507763472740256xy^{40}z^{7}+1447067937814396112076912xy^{39}z^{8}+373996335499904254371129720xy^{38}z^{9}+29212818247451634120832094208xy^{37}z^{10}+1610172751163426910353464743456xy^{36}z^{11}+68786428984310292970593568519584xy^{35}z^{12}+2301505618422812937626055291687846xy^{34}z^{13}+60350722962274156785254554654365696xy^{33}z^{14}+1235758855265920651835405711103724800xy^{32}z^{15}+19526553297990631264035515333569338816xy^{31}z^{16}+230068415460325192805423198954590684272xy^{30}z^{17}+1800170159858064702901217761529550667776xy^{29}z^{18}+3917715865617507322736154118058518425984xy^{28}z^{19}-137460816127613023730451658479743512513920xy^{27}z^{20}-2679968428892809664467677263601741744618735xy^{26}z^{21}-30171093370200438429600288146722243824119808xy^{25}z^{22}-247674427056681309144586836984703033475252640xy^{24}z^{23}-1548265289782521045528927587915386173448660944xy^{23}z^{24}-7136150859449545761136456473022584562054841040xy^{22}z^{25}-19740530348904918871920192414326220065638883328xy^{21}z^{26}+21307252404665724377636323515245491815969801312xy^{20}z^{27}+666750853499001051043940440589621789012940031200xy^{19}z^{28}+4858803425862220046269171460788913939682223357566xy^{18}z^{29}+23884654685009582643420828626740533685088225138688xy^{17}z^{30}+88894638067173216125377345651949202634119517510272xy^{16}z^{31}+251366681907839515421926021859367054506442173724912xy^{15}z^{32}+488550370330587632424088646760913395196646508178740xy^{14}z^{33}+296211757028618079024348606051627111219319168653312xy^{13}z^{34}-2321746319863976168924858410417677842021431517837472xy^{12}z^{35}-12338374125687437870418493599859757947005688163802336xy^{11}z^{36}-38148123167052823844869141461212082392953354830230841xy^{10}z^{37}-87814814116544350371341629397726153997406124502521856xy^{9}z^{38}-159271224451852146971273025265877739706940190245521056xy^{8}z^{39}-230156331737067936399533241428343136687829310966041136xy^{7}z^{40}-262016138672943014816568089774084452425553411135004232xy^{6}z^{41}-2277744928293259143404005337913302669848227043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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.
