Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 300x - 1375 $ |
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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 40 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -2^{12}\cdot3\cdot5^3\,\frac{(y^{2}+3375z^{2})(1012x^{2}y^{23}+39417150x^{2}y^{22}z+6173442000x^{2}y^{21}z^{2}-6827262187500x^{2}y^{20}z^{3}+768052621125000x^{2}y^{19}z^{4}+26231446961718750x^{2}y^{18}z^{5}-10526406429304687500x^{2}y^{17}z^{6}+465659652821484375000x^{2}y^{16}z^{7}+113950743653583984375000x^{2}y^{15}z^{8}+1192558780878881835937500x^{2}y^{14}z^{9}-532257326331569824218750000x^{2}y^{13}z^{10}-20248085888931280517578125000x^{2}y^{12}z^{11}+5536269811716345703125000000000x^{2}y^{11}z^{12}+119411544462115192794799804687500x^{2}y^{10}z^{13}-65968941436313746021270751953125000x^{2}y^{9}z^{14}+7654287025934360465240478515625000000x^{2}y^{8}z^{15}-611760102944016456785917282104492187500x^{2}y^{7}z^{16}+27405369846260323199781775474548339843750x^{2}y^{6}z^{17}-311963711919301845930576324462890625000000x^{2}y^{5}z^{18}-18277981752663225170528143644332885742187500x^{2}y^{4}z^{19}+495909355205363200062118470668792724609375000x^{2}y^{3}z^{20}-160121722012419856572523713111877441406250x^{2}y^{2}z^{21}-654925742809915598016232252120971679687500x^{2}yz^{22}-1164887684839770826511085033416748046875000x^{2}z^{23}+8xy^{24}+1882615xy^{23}z+4032815250xy^{22}z^{2}-2067792738750xy^{21}z^{3}+249841761187500xy^{20}z^{4}+14853093594609375xy^{19}z^{5}-2107231712261718750xy^{18}z^{6}-115372341985429687500xy^{17}z^{7}+8945790063099609375000xy^{16}z^{8}+747491626771940917968750xy^{15}z^{9}-73795675328889038085937500xy^{14}z^{10}-8803011452077842407226562500xy^{13}z^{11}-455826204382453582763671875000xy^{12}z^{12}+95504321490062299461364746093750xy^{11}z^{13}+8694218558628101503372192382812500xy^{10}z^{14}-1983565307921217064590454101562500000xy^{9}z^{15}+182888623821573381556034088134765625000xy^{8}z^{16}-12231104314187761236830055713653564453125xy^{7}z^{17}+505634041384802927953854203224182128906250xy^{6}z^{18}-5400846869736071673638150095939636230468750xy^{5}z^{19}-352183508041647708420742303133010864257812500xy^{4}z^{20}+9556954753280946087367194704711437225341796875xy^{3}z^{21}+805785888661387153202667832374572753906250xy^{2}z^{22}+3274628714049577990081161260604858398437500xyz^{23}+5824438424198854132555425167083740234375000xz^{24}+57150y^{24}z+527030200y^{23}z^{2}-211038708750y^{22}z^{3}+24148760512500y^{21}z^{4}+2204080330781250y^{20}z^{5}-434128525931250000y^{19}z^{6}-48697587921972656250y^{18}z^{7}+3342867975395507812500y^{17}z^{8}+241883011784926757812500y^{16}z^{9}-27684462664489746093750000y^{15}z^{10}-2056131277051920776367187500y^{14}z^{11}+127500654206269390869140625000y^{13}z^{12}-3776656311322049789428710937500y^{12}z^{13}-1115084415221940673828125000000000y^{11}z^{14}+296725141049856156034469604492187500y^{10}z^{15}-32683314016452117064189910888671875000y^{9}z^{16}+1887954631929541675581336021423339843750y^{8}z^{17}-59809070913212631708061695098876953125000y^{7}z^{18}+1089591293461257370798364281654357910156250y^{6}z^{19}+1240794952292269992522150278091430664062500y^{5}z^{20}-1303594210299363474903842434287071228027343750y^{4}z^{21}+35391901739171276692122593522071838378906250000y^{3}z^{22}+43981700767422581854043528437614440917968750y^{2}z^{23}+180104579272726789454463869333267211914062500yz^{24}+320344113330936977290548384189605712890625000z^{25})}{1161900x^{2}y^{24}z-29757281850000x^{2}y^{22}z^{3}+33415489793784375000x^{2}y^{20}z^{5}-1063237511193644531250000x^{2}y^{18}z^{7}+4582823775748120239257812500x^{2}y^{16}z^{9}-14814471411970013012695312500000x^{2}y^{14}z^{11}+67974904274566768135070800781250000x^{2}y^{12}z^{13}-389609341069988239854812622070312500000x^{2}y^{10}z^{15}+1951939275594078313365250825881958007812500x^{2}y^{8}z^{17}-7294527353339684151729539036750793457031250000x^{2}y^{6}z^{19}+18577615718983467620180731080472469329833984375000x^{2}y^{4}z^{21}-28607434606361009050651965150609612464904785156250000x^{2}y^{2}z^{23}+20065410778089374972734353299892973154783248901367187500x^{2}z^{25}+xy^{26}-505792125xy^{24}z^{2}+4338423015468750xy^{22}z^{4}-1741717341711949218750xy^{20}z^{6}+15592484056546834716796875xy^{18}z^{8}-43805300697736671478271484375xy^{16}z^{10}+49310015787476553543090820312500xy^{14}z^{12}+292971543989959922590255737304687500xy^{12}z^{14}-3842230255811218450719416141510009765625xy^{10}z^{16}+26098850483566028504741974174976348876953125xy^{8}z^{18}-114344064305379665607733385637402534484863281250xy^{6}z^{20}+320706456697035981261274141492322087287902832031250xy^{4}z^{22}-526631047545163223244318906727130524814128875732421875xy^{2}z^{24}+386670687979079050543086893119834712706506252288818359375xz^{26}-1600y^{26}z+146472120000y^{24}z^{3}-448268979330000000y^{22}z^{5}+52060309528218750000000y^{20}z^{7}-16691573454296484375000000y^{18}z^{9}-773586724485139013671875000000y^{16}z^{11}+4827277069259995766601562500000000y^{14}z^{13}-23389982028882862728881835937500000000y^{12}z^{15}+93042073477026679130344390869140625000000y^{10}z^{17}-266814794606393385160052776336669921875000000y^{8}z^{19}+441501114530899050284788012504577636718750000000y^{6}z^{21}-81442629401558781158751323819160461425781250000000y^{4}z^{23}-1091229020061907711552884788252413272857666015625000000y^{2}z^{25}+1431718170553734201606475754524581134319305419921875000000z^{27}}$ 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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.
