Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 275x - 1750 $ |
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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{1}{5^2}\cdot\frac{9384760173473061894x^{2}y^{30}-100732725279351470965320x^{2}y^{29}z+184405244402058415360438975x^{2}y^{28}z^{2}-144517889256730989632255415000x^{2}y^{27}z^{3}+66155227567137803725043973350000x^{2}y^{26}z^{4}-20330942321523437125641985445625000x^{2}y^{25}z^{5}+4492950970757733704367458437926562500x^{2}y^{24}z^{6}-733529590696846316704251248640000000000x^{2}y^{23}z^{7}+87228189749992551300086113982725585937500x^{2}y^{22}z^{8}-6511790784877607443639168697504003906250000x^{2}y^{21}z^{9}+125974868678960308003701509099780621337890625x^{2}y^{20}z^{10}+77467989551098775700902014578506929321289062500x^{2}y^{19}z^{11}-7079724500361026478368171306529113600158691406250x^{2}y^{18}z^{12}+1984909131391722698600291463664831257705688476562500x^{2}y^{17}z^{13}+117125724584833325459706841985030199521923065185546875x^{2}y^{16}z^{14}+30400805411930040506209774933427914686126708984375000000x^{2}y^{15}z^{15}+4879974031307340021185137942206793781038784980773925781250x^{2}y^{14}z^{16}+518657920113401693065550014415567920164949893951416015625000x^{2}y^{13}z^{17}+68198228207670006089150430962326768375049848854541778564453125x^{2}y^{12}z^{18}+6224113199523503854860109642844683695172779858112335205078125000x^{2}y^{11}z^{19}+557361995616955812629071149939175684404111586511135101318359375000x^{2}y^{10}z^{20}+44485527171159092333223581842703636156970018725842237472534179687500x^{2}y^{9}z^{21}+2913389669006683535817458866068358102962727572396397590637207031250000x^{2}y^{8}z^{22}+188865794841795428823758688214753498033857872374355792999267578125000000x^{2}y^{7}z^{23}+9741976397121264422571766348609226831691001874365611001849174499511718750x^{2}y^{6}z^{24}+469547959454007964472518954558760829956005568645778112113475799560546875000x^{2}y^{5}z^{25}+19966977781800013734790730973137240910173858631913753924891352653503417968750x^{2}y^{4}z^{26}+631917123427421845549041562670638563978893288694853254128247499465942382812500x^{2}y^{3}z^{27}+22664758788740846483849741655345067284119836286998634022893384099006652832031250x^{2}y^{2}z^{28}+355496055137042976130214969600902209205516133002970491361338645219802856445312500x^{2}yz^{29}+10832948545111847443747382413492224253814425535040442127865389920771121978759765625x^{2}z^{30}-191615060804159412xy^{31}+6049905133662429286041xy^{30}z-17002751852654915519840700xy^{29}z^{2}+16941062967000889015731819750xy^{28}z^{3}-9194726815415275934056404525000xy^{27}z^{4}+3249724654335281853157532298156250xy^{26}z^{5}-816781938508037307998342641509375000xy^{25}z^{6}+152242373724432226245528323116476562500xy^{24}z^{7}-21150378015778950437530919787870703125000xy^{23}z^{8}+2102479878703243558990767957452389160156250xy^{22}z^{9}-104889043794238389058452744353490087890625000xy^{21}z^{10}-3581313917977276056954660069528025939941406250xy^{20}z^{11}+2844813092157206825323945267097171310424804687500xy^{19}z^{12}-128369922006806932895197066265617551113128662109375xy^{18}z^{13}+57217481488747845962008783919201841307067871093750000xy^{17}z^{14}+5173143184866675955873636438883719209845542907714843750xy^{16}z^{15}+922965930558859636172680761405652538934946060180664062500xy^{15}z^{16}+145065836015791831694991033822216525493992507457733154296875xy^{14}z^{17}+14799761209887837184422918222265643455527251958847045898437500xy^{13}z^{18}+1787068471854838005616992574866216860470897689461708068847656250xy^{12}z^{19}+159328597351603775974875637099149524740354554355144500732421875000xy^{11}z^{20}+13451241540040805840528152294191683188037044913507997989654541015625xy^{10}z^{21}+1041139579885431666857094102959126609883555561583489179611206054687500xy^{9}z^{22}+65854022548892384692662201387274180911970407064305618405342102050781250xy^{8}z^{23}+4125544557494112152805045333398133791189092936122324317693710327148437500xy^{7}z^{24}+208546412078587329756210009609066395710115246521032531745731830596923828125xy^{6}z^{25}+9718340567685707949808738129157704126186651227039692457765340805053710937500xy^{5}z^{26}+408596700207298532092368447968663345586751892438456707168370485305786132812500xy^{4}z^{27}+12527532315038876623789242105968340808431712433170287113171070814132690429687500xy^{3}z^{28}+446994457005794300335050960018584409311378658531631344885681755840778350830078125xy^{2}z^{29}+6804953701134612515254626474472232307944838669970295086386613547801971435546875000xyz^{30}+207365770255429866498009591038607357461855744649595578721346100792288780212402343750xz^{31}+1786060237907601y^{32}-283076691287993651988y^{31}z+1399246633860177336962040y^{30}z^{2}-1820323777060740066993342000y^{29}z^{3}+1156631509054677495181747292500y^{28}z^{4}-453629042732147384586725824500000y^{27}z^{5}+122673299283263495495717992169687500y^{26}z^{6}-24144382848801928256695027203703125000y^{25}z^{7}+3509226697795855295200262587756171875000y^{24}z^{8}-359275814846244480576059652240826171875000y^{23}z^{9}+21575897348746938307214871319239355468750000y^{22}z^{10}+1060113160845705833142028780806967895507812500y^{21}z^{11}-2642877489189366789372571594830544834899902343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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.
