Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 14 x^{2} + 21 x y + 2 y^{2} + y z + z^{2} + w^{2} $ |
| $=$ | $28 x^{2} - 14 x y + 3 y^{2} - 2 y z - 2 z^{2}$ |
Singular plane model Singular plane model
$ 0 $ | $=$ | $ x^{4} + 4 x^{3} y - 22 x^{2} y^{2} + 4 x^{2} z^{2} - 52 x y^{3} + 8 x y z^{2} + 365 y^{4} + 60 y^{2} z^{2} + 4 z^{4} $ |
This modular curve has no real points, and therefore no rational points.
Maps between models of this curve
Birational map from embedded model to plane model:
$\displaystyle X$ |
$=$ |
$\displaystyle z$ |
$\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{2}y$ |
$\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{2}w$ |
Maps to other modular curves
$j$-invariant map
of degree 48 from the embedded model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^8}{7^2}\cdot\frac{582882970420288743285419136xz^{11}-1690728734233252975060199232xz^{9}w^{2}-13154504127162839997682190400xz^{7}w^{4}-124769502965852842829368000xz^{5}w^{6}+2842125718890798972086000000xz^{3}w^{8}-68172141993279968791000000xzw^{10}+265571673086880851900444676y^{2}z^{10}-3766570941381633109802625975y^{2}z^{8}w^{2}-11384886657168945494448462000y^{2}z^{6}w^{4}+11878279557337306264347875000y^{2}z^{4}w^{6}-827053058161860630658687500y^{2}z^{2}w^{8}-4298536589914304796875000y^{2}w^{10}-114581333146594780841431392yz^{11}-1946443162891206463037001252yz^{9}w^{2}-850190382252742993626276000yz^{7}w^{4}+7865204921892372944908032000yz^{5}w^{6}-1588435793439227072539850000yz^{3}w^{8}+8794376151277667999000000yzw^{10}-136729741927086828129501864z^{12}-77670711123782872767563052z^{10}w^{2}+2195145931351928129080986690z^{8}w^{4}+1142074507496699768098212000z^{6}w^{6}-122908264468280589807250000z^{4}w^{8}-61474427765535717983875000z^{2}w^{10}+15612176486917674375000w^{12}}{1762306788874644726486528xz^{11}+3380523788224938117176064xz^{9}w^{2}+2313551447296442510438400xz^{7}w^{4}+607462401129542565936000xz^{5}w^{6}+11611883763236118600000xz^{3}w^{8}-13076377100438253000000xzw^{10}+802937787110750874982448y^{2}z^{10}+1721592917845238732386400y^{2}z^{8}w^{2}+1247926526106163486814000y^{2}z^{6}w^{4}+330671331345284998843750y^{2}z^{4}w^{6}+775739322052576750000y^{2}z^{2}w^{8}-8620909518963641796875y^{2}w^{10}-346428822816613094002816yz^{11}-371298416156086431830496yz^{9}w^{2}+17611891613067426085600yz^{7}w^{4}+170968898583030007441000yz^{5}w^{6}+77975217759903010050000yz^{3}w^{8}+10932956992582349187500yzw^{10}-413393021699431075221472z^{12}-663658335272741607647296z^{10}w^{2}-301184849582567000890280z^{8}w^{4}+21060682622116436189000z^{6}w^{6}+41566461671631248312500z^{4}w^{8}+5052421886308948437500z^{2}w^{10}-688823061297910468750w^{12}}$ |
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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.