Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ 26 x^{4} - 13 x^{3} y + x^{3} z - 6 x^{2} y^{2} + 3 x^{2} y z + 3 x^{2} z^{2} - x y^{3} + 3 x y^{2} z + \cdots + 2 z^{4} $ |
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This modular curve has 2 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
Maps to other modular curves
$j$-invariant map
of degree 48 from the canonical model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{13^3}{3^4}\cdot\frac{17098317290379x^{3}y^{9}-599623379088903x^{3}y^{8}z+6913032704090604x^{3}y^{7}z^{2}-23266404172802700x^{3}y^{6}z^{3}-26830540115986230x^{3}y^{5}z^{4}+20832728320947582x^{3}y^{4}z^{5}+35450524299909564x^{3}y^{3}z^{6}+13197287864277252x^{3}y^{2}z^{7}-71244668031741x^{3}yz^{8}-623875079838447x^{3}z^{9}+5642560777048x^{2}y^{10}-204685187981937x^{2}y^{9}z+2420538566043429x^{2}y^{8}z^{2}-9181040421753252x^{2}y^{7}z^{3}-7327594387261980x^{2}y^{6}z^{4}+19571459263344450x^{2}y^{5}z^{5}+27944905233767958x^{2}y^{4}z^{6}+10024917129506412x^{2}y^{3}z^{7}-3318624408353508x^{2}y^{2}z^{8}-3176970320650905x^{2}yz^{9}-584382358086291x^{2}z^{10}+774747081095xy^{11}-31214634090185xy^{10}z+411755712893850xy^{9}z^{2}-2076033042759780xy^{8}z^{3}-291451151293614xy^{7}z^{4}+11682167922526698xy^{6}z^{5}+19068770450126808xy^{5}z^{6}+8266047601135428xy^{4}z^{7}-5755247948637297xy^{3}z^{8}-7098283712066697xy^{2}z^{9}-2410573456103130xyz^{10}-230619203695224xz^{11}-2471326208y^{12}-863714824583y^{11}z+24104105545585y^{10}z^{2}-238848519877812y^{9}z^{3}+126003910732362y^{8}z^{4}+3001072397594310y^{7}z^{5}+6813317492337006y^{6}z^{6}+5241158822537532y^{5}z^{7}-1715767919823744y^{4}z^{8}-5131505035314711y^{3}z^{9}-3000245188213863y^{2}z^{10}-650259203699376yz^{11}-26657654161986z^{12}}{90096063186649x^{3}y^{9}-118762204338973x^{3}y^{8}z-280504329050348x^{3}y^{7}z^{2}-147235720069204x^{3}y^{6}z^{3}+183754399462270x^{3}y^{5}z^{4}+317845111950938x^{3}y^{4}z^{5}+223303819295908x^{3}y^{3}z^{6}+88084243536380x^{3}y^{2}z^{7}+19537535348721x^{3}yz^{8}+2084935866651x^{3}z^{9}+29968919521736x^{2}y^{10}-61240960801787x^{2}y^{9}z-116694561686521x^{2}y^{8}z^{2}+6324298726564x^{2}y^{7}z^{3}+218238387729596x^{2}y^{6}z^{4}+272997297540838x^{2}y^{5}z^{5}+161312787584546x^{2}y^{4}z^{6}+40965314604916x^{2}y^{3}z^{7}-4878960158780x^{2}y^{2}z^{8}-5497123292931x^{2}yz^{9}-989030179953x^{2}z^{10}+4161792762413xy^{11}-21571217659251xy^{10}z-35914099459602xy^{9}z^{2}+34284367764036xy^{8}z^{3}+161755443990582xy^{7}z^{4}+192325314257310xy^{6}z^{5}+93875284943544xy^{5}z^{6}-18633455066148xy^{4}z^{7}-54034873433451xy^{3}z^{8}-33558167296547xy^{2}z^{9}-10184508908958xyz^{10}-1297343676456xz^{11}-4161792762413y^{11}z-8397701862485y^{10}z^{2}+7058997074740y^{9}z^{3}+51347858814590y^{8}z^{4}+79647071523058y^{7}z^{5}+48814150555274y^{6}z^{6}-10295119079804y^{5}z^{7}-42585650331536y^{4}z^{8}-35501622461837y^{3}z^{9}-16004395542925y^{2}z^{10}-4015699137264yz^{11}-442426476438z^{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.
