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{2^2}{5^4}\cdot\frac{41950818x^{2}y^{14}+237864888x^{2}y^{13}z-5297015889881x^{2}y^{12}z^{2}-1895175016704000x^{2}y^{11}z^{3}-479871677208024500x^{2}y^{10}z^{4}-96331475372767162500x^{2}y^{9}z^{5}-14446701465618288468750x^{2}y^{8}z^{6}-1670374972474209168750000x^{2}y^{7}z^{7}-158154962953093653683593750x^{2}y^{6}z^{8}-12345260334067283586328125000x^{2}y^{5}z^{9}-772360678102218118439941406250x^{2}y^{4}z^{10}-38561387551347361307739257812500x^{2}y^{3}z^{11}-1521045448475040077454162597656250x^{2}y^{2}z^{12}-41766100943016276081106567382812500x^{2}yz^{13}-558460284039889166572483062744140625x^{2}z^{14}-2792556xy^{15}+889333515xy^{14}z-72924634164xy^{13}z^{2}-252282358155370xy^{12}z^{3}-86323842058134000xy^{11}z^{4}-18342741401850276875xy^{10}z^{5}-3074778597567951187500xy^{9}z^{6}-410751824656488531718750xy^{8}z^{7}-43631131768587176554687500xy^{7}z^{8}-3816950506776181127275390625xy^{6}z^{9}-278814569834292428170898437500xy^{5}z^{10}-16572703361148669732934570312500xy^{4}z^{11}-788818087501518470166870117187500xy^{3}z^{12}-29793584199813223008357696533203125xy^{2}z^{13}-799492368725661887188934326171875000xyz^{14}-10690122497558871934275169372558593750xz^{15}+59319y^{16}-227543148y^{15}z-84308413672y^{14}z^{2}-27970145103480y^{13}z^{3}-11064573850320650y^{12}z^{4}-2890731723888255000y^{11}z^{5}-501481384910629081250y^{10}z^{6}-66477193482125762812500y^{9}z^{7}-7243668066812679616406250y^{8}z^{8}-645336798614118740976562500y^{7}z^{9}-46785013971607409983203125000y^{6}z^{10}-2817172955684498461479492187500y^{5}z^{11}-139887213944635044242303466796875y^{4}z^{12}-5465228125268469546260375976562500y^{3}z^{13}-164994624480182035187535095214843750y^{2}z^{14}-3818313592954984605806350708007812500yz^{15}-51055196571599799149815464019775390625z^{16}}{148x^{2}y^{14}+13344365x^{2}y^{12}z^{2}-140883235592x^{2}y^{10}z^{4}-1216803079551800x^{2}y^{8}z^{6}+16962973583777825000x^{2}y^{6}z^{8}-21488293903263275390625x^{2}y^{4}z^{10}-280750423557606870312500000x^{2}y^{2}z^{12}+802583367157625984185791015625x^{2}z^{14}+10578xy^{14}z+275517156xy^{12}z^{3}-5023329818544xy^{10}z^{5}-6972679564186500xy^{8}z^{7}+339601281840905343750xy^{6}z^{9}-834239755870712421875000xy^{4}z^{11}-4400465785768203929443359375xy^{2}z^{13}+15363159663481860158142089843750xz^{15}+y^{16}+448636y^{14}z^{2}-600802582y^{12}z^{4}-92755594497780y^{10}z^{6}+589741599142245625y^{8}z^{8}+1508053850098507187500y^{6}z^{10}-16973918068398848593750000y^{4}z^{12}+11610691684896254956054687500y^{2}z^{14}+73373259919056062767486572265625z^{16}}$ |
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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.
