Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 24x + 56 $ |
![Copy content]()
![Toggle raw display]()
This modular curve is an elliptic curve, but the rank has not been computed
Maps to other modular curves
$j$-invariant map
of degree 96 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{1}{2^6\cdot3^6}\cdot\frac{48x^{2}y^{30}+93312x^{2}y^{28}z^{2}-33592320x^{2}y^{26}z^{4}-3851937275904x^{2}y^{24}z^{6}+1266051435134976x^{2}y^{22}z^{8}-12862342823262289920x^{2}y^{20}z^{10}-24244030489958874611712x^{2}y^{18}z^{12}+12008584070097916775104512x^{2}y^{16}z^{14}-1143666561233807533878018048x^{2}y^{14}z^{16}-68949369250643486876689760256x^{2}y^{12}z^{18}+5983416926391023541696470188032x^{2}y^{10}z^{20}-59046643829758819156652351029248x^{2}y^{8}z^{22}+15212703877594496914906822974898176x^{2}y^{6}z^{24}-129290407179696595904137318285443072x^{2}y^{4}z^{26}-29405065906854270953324094403897196544x^{2}y^{2}z^{28}+454034544748725490855096936058918535168x^{2}z^{30}-96xy^{30}z+5412096xy^{28}z^{3}+12241041408xy^{26}z^{5}+27939243147264xy^{24}z^{7}+93709121252622336xy^{22}z^{9}-227442078550645014528xy^{20}z^{11}-158119931506129958338560xy^{18}z^{13}+53359158646669320589934592xy^{16}z^{15}-2326626964717237267184222208xy^{14}z^{17}+247171155540851057896080801792xy^{12}z^{19}-38872583963244525196446145708032xy^{10}z^{21}-1321470352616209426794821883789312xy^{8}z^{23}+159535601304806363096888247941332992xy^{6}z^{25}-499837355796444904264630128756129792xy^{4}z^{27}-29612957181922368705547124136524906496xy^{2}z^{29}-908069089497450981710193872117837070336xz^{31}-y^{32}-21120y^{30}z^{2}-37698048y^{28}z^{4}-202575126528y^{26}z^{6}+334319905751040y^{24}z^{8}+825236085435531264y^{22}z^{10}-2104740368088985239552y^{20}z^{12}+161890600828535706746880y^{18}z^{14}-18771979010690013154246656y^{16}z^{16}-10800148763885844592739745792y^{14}z^{18}+2545849726065150540621501431808y^{12}z^{20}-93512103286048304970564693393408y^{10}z^{22}-4954788374433291516147167970459648y^{8}z^{24}+270340248814453057422323091001835520y^{6}z^{26}-3042655636953455373585206765804322816y^{4}z^{28}+136561468689177101238061308810557915136y^{2}z^{30}-3654728615697158484080862699595140956160z^{32}}{z^{4}y^{4}(y^{2}-216z^{2})^{6}(24x^{2}y^{10}-104976x^{2}y^{8}z^{2}-110854656x^{2}y^{6}z^{4}+48977602560x^{2}y^{4}z^{6}-228509902503936x^{2}z^{10}+456xy^{10}z+1539648xy^{8}z^{3}-1169012736xy^{6}z^{5}-104485552128xy^{4}z^{7}+38084983750656xy^{2}z^{9}-914039610015744xz^{11}-y^{12}-9552y^{10}z^{2}+13110336y^{8}z^{4}+3184551936y^{6}z^{6}-1286478360576y^{4}z^{8}+76169967501312y^{2}z^{10}-914039610015744z^{12})}$ |
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.
