Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 49x $ |
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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{2^6}{7^4}\cdot\frac{632745313200x^{2}y^{14}+172462181984064x^{2}y^{13}z-3969576736755642x^{2}y^{12}z^{2}-530784602100006912x^{2}y^{11}z^{3}+20149798431645870624x^{2}y^{10}z^{4}+154388733303546457632x^{2}y^{9}z^{5}-23232071252673648782193x^{2}y^{8}z^{6}+276838713422357823571968x^{2}y^{7}z^{7}+4086941002054009916454288x^{2}y^{6}z^{8}-103970982456774842504340672x^{2}y^{5}z^{9}+1609813481002226284562552075x^{2}y^{4}z^{10}-2267258360432973407689265664x^{2}y^{3}z^{11}-180636593507196269376211321680x^{2}y^{2}z^{12}+1456357360200482410339328906400x^{2}yz^{13}-3254665337392327171898998447125x^{2}z^{14}+45541980000xy^{15}+36958123540772xy^{14}z+685723085873664xy^{13}z^{2}-188137160368426080xy^{12}z^{3}+2811976110208472256xy^{11}z^{4}+222144130351333763685xy^{10}z^{5}-7991747764289570760192xy^{9}z^{6}+1914864313389920784864xy^{8}z^{7}+2909918649557823288656544xy^{7}z^{8}-88572057748174707264801712xy^{6}z^{9}+144379661814555098566430208xy^{5}z^{10}+14850984273243469532553743280xy^{4}z^{11}-134154990995500279702288591200xy^{3}z^{12}+332915190774221102727992326875xy^{2}z^{13}+1684546875y^{16}+5756009796096y^{15}z+562795829076096y^{14}z^{2}-35630658141462720y^{13}z^{3}-813918043966585908y^{12}z^{4}+75825332429285698560y^{11}z^{5}-619993159969543497648y^{10}z^{6}-28917878074657097672160y^{9}z^{7}+1201417258644319998735636y^{8}z^{8}-2673949492034390248573440y^{7}z^{9}-217482738332783378647114944y^{6}z^{10}+2003731841624202990607364064y^{5}z^{11}-4188469954387999552968522778y^{4}z^{12}-9373164621668477280157807104y^{3}z^{13}+50488182529420309984823713200y^{2}z^{14}-178060991998145470067797020000yz^{15}+322727564630785089109159546875z^{16}}{659016x^{2}y^{14}+4015992302x^{2}y^{12}z^{2}+28566266294448x^{2}y^{10}z^{4}+37160271557734787x^{2}y^{8}z^{6}-18117389721431437416x^{2}y^{6}z^{8}-17798586158388501810225x^{2}y^{4}z^{10}+452834416098315937408968x^{2}y^{2}z^{12}+287095206070427670350748495x^{2}z^{14}-24324300xy^{14}z-147408983568xy^{12}z^{3}-203473350111679xy^{10}z^{5}+354641572173300048xy^{8}z^{7}+390996083417563815408xy^{6}z^{9}-36856569618674714027448xy^{4}z^{11}-29298570293215038156352641xy^{2}z^{13}-6561y^{16}+317693376y^{14}z^{2}+314530094620y^{12}z^{4}-3072034038684744y^{10}z^{6}-3628427171092500028y^{8}z^{8}+570651512210586634464y^{6}z^{10}+477462985667142095725902y^{4}z^{12}+52584380166387070451016y^{2}z^{14}-1256964459087896244884961z^{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.
