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 24 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -\frac{2^4}{5^2}\cdot\frac{5759964x^{2}y^{14}+10517262840x^{2}y^{13}z+6312342305725x^{2}y^{12}z^{2}+2021068724310000x^{2}y^{11}z^{3}+420346584739050000x^{2}y^{10}z^{4}+62829587089141875000x^{2}y^{9}z^{5}+7142535988510439062500x^{2}y^{8}z^{6}+637396986158486015625000x^{2}y^{7}z^{7}+45344031911317968750000000x^{2}y^{6}z^{8}+2578751590625481181640625000x^{2}y^{5}z^{9}+116035485186543546575927734375x^{2}y^{4}z^{10}+4013060817595636519775390625000x^{2}y^{3}z^{11}+100476374383928222479248046875000x^{2}y^{2}z^{12}+1615315094485050051727294921875000x^{2}yz^{13}+12424608629420943271350860595703125x^{2}z^{14}+285768xy^{15}+1017134046xy^{14}z+822416251200xy^{13}z^{2}+321509082398500xy^{12}z^{3}+78535246361175000xy^{11}z^{4}+13552800644129125000xy^{10}z^{5}+1767982016022618750000xy^{9}z^{6}+181326064172934117187500xy^{8}z^{7}+14942674292209094531250000xy^{7}z^{8}+998641417646239586425781250xy^{6}z^{9}+54065830117075359228515625000xy^{5}z^{10}+2341791201418576233154296875000xy^{4}z^{11}+78778260259019481793212890625000xy^{3}z^{12}+1938405963312663502155303955078125xy^{2}z^{13}+30920580613693374678039550781250000xyz^{14}+237833543456152979395866394042968750xz^{15}+9261y^{16}+84200472y^{15}z+96540212620y^{14}z^{2}+44868567525000y^{13}z^{3}+12025209561758750y^{12}z^{4}+2180941405771125000y^{11}z^{5}+291741878262892187500y^{10}z^{6}+30259159443281343750000y^{9}z^{7}+2506937331978460751953125y^{8}z^{8}+168734116933672042968750000y^{7}z^{9}+9292424446425025717773437500y^{6}z^{10}+418182084585389501953125000000y^{5}z^{11}+15244418597049578423461914062500y^{4}z^{12}+441905371870854846954345703125000y^{3}z^{13}+9762767360024785560379028320312500y^{2}z^{14}+147674296688428060283660888671875000yz^{15}+1135874571619436018822193145751953125z^{16}}{16x^{2}y^{14}-630716x^{2}y^{12}z^{2}+5005377000x^{2}y^{10}z^{4}-26205518468750x^{2}y^{8}z^{6}+102150598906250000x^{2}y^{6}z^{8}-270136661212158203125x^{2}y^{4}z^{10}+424866958708618164062500x^{2}y^{2}z^{12}-298648384200626373291015625x^{2}z^{14}+984xy^{14}z-7738120xy^{12}z^{3}+52377686250xy^{10}z^{5}-343073899687500xy^{8}z^{7}+1579525244335937500xy^{6}z^{9}-4624915920361328125000xy^{4}z^{11}+7770539678013763427734375xy^{2}z^{13}-5716767874107017517089843750xz^{15}-y^{16}-3704y^{14}z^{2}+190712300y^{12}z^{4}-1076563300000y^{10}z^{6}+3166847083593750y^{8}z^{8}-4350119798828125000y^{6}z^{10}-4229736648864746093750y^{4}z^{12}+24970708537469482421875000y^{2}z^{14}-27302840321067142486572265625z^{16}}$ |
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Cover information
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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.
