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 -2^6\,\frac{14056582102920x^{2}y^{14}+114680568981096000x^{2}y^{13}z+119757623131749843750x^{2}y^{12}z^{2}+52981103966552064000000x^{2}y^{11}z^{3}+14272569287502559595625000x^{2}y^{10}z^{4}+2710170692452395990562500000x^{2}y^{9}z^{5}+391092191367802513626591796875x^{2}y^{8}z^{6}+44495699913839998227375000000000x^{2}y^{7}z^{7}+4137704528776156488338789062500000x^{2}y^{6}z^{8}+310037817591813143749658203125000000x^{2}y^{5}z^{9}+19681097408109479771696526336669921875x^{2}y^{4}z^{10}+959182913024483656339842773437500000000x^{2}y^{3}z^{11}+41210216936821017123365455856323242187500x^{2}y^{2}z^{12}+1084469150646597030664536941528320312500000x^{2}yz^{13}+28968623525609865222507777278423309326171875x^{2}z^{14}+292505130720xy^{15}+7898724540284900xy^{14}z+13430797175471160000xy^{13}z^{2}+7552835176971365675000xy^{12}z^{3}+2407108264442520885000000xy^{11}z^{4}+524726302011595971045703125xy^{10}z^{5}+85637938961427895946250000000xy^{9}z^{6}+11033535686481185408867871093750xy^{8}z^{7}+1145972495955092631085195312500000xy^{7}z^{8}+99295204803869140803746533203125000xy^{6}z^{9}+6987263568926095329128056640625000000xy^{5}z^{10}+423764038427072809357385345458984375000xy^{4}z^{11}+19676491108440572092303049926757812500000xy^{3}z^{12}+823996395273779157922656532573699951171875xy^{2}z^{13}+20759055561429457584554630584716796875000000xyz^{14}+554521320360027094974922227215766906738281250xz^{15}+2729559627y^{16}+404137775596800y^{15}z+1336832878419654000y^{14}z^{2}+968174867480349000000y^{13}z^{3}+348741128841492689187500y^{12}z^{4}+81306310699702615500000000y^{11}z^{5}+13794058521232122112640625000y^{10}z^{6}+1809216522358461378857812500000y^{9}z^{7}+191640954217454620859141601562500y^{8}z^{8}+16474183147575469245253125000000000y^{7}z^{9}+1200880458761648316273342773437500000y^{6}z^{10}+70233605861973869894576147460937500000y^{5}z^{11}+3642259033157229191758539360046386718750y^{4}z^{12}+138059717842055380255297961425781250000000y^{3}z^{13}+5112988265142499523964823402404785156250000y^{2}z^{14}+99143640549634872081706035232543945312500000yz^{15}+2648350851039284427661138976275920867919921875z^{16}}{8602200x^{2}y^{14}-259450677171250x^{2}y^{12}z^{2}-31000168675919375000x^{2}y^{10}z^{4}+1467032387720075849609375x^{2}y^{8}z^{6}-829472652427526221972656250000x^{2}y^{6}z^{8}-21567793598038053020829010009765625x^{2}y^{4}z^{10}-151268976335257599962680130004882812500x^{2}y^{2}z^{12}-312802327239065600000015642642974853515625x^{2}z^{14}-4801315500xy^{14}z+25234488460275000xy^{12}z^{3}+1548725416006212890625xy^{10}z^{5}-201687011915663548925781250xy^{8}z^{7}-31276941571193669802490234375000xy^{6}z^{9}-564297501423697548328948974609375000xy^{4}z^{11}-3275104118741401600373824405670166015625xy^{2}z^{13}-5987704571428863999999843573570251464843750xz^{15}-6561y^{16}+1465299918000y^{14}z^{2}-898325979203562500y^{12}z^{4}+125457116684903484375000y^{10}z^{6}-17571247927624247581054687500y^{8}z^{8}-810190746412080693401367187500000y^{6}z^{10}-8230077227178387150635169982910156250y^{4}z^{12}-28357822487986176006518463134765625000000y^{2}z^{14}-28596812990382079999997262537479400634765625z^{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.
