Properties

Label 33600ey
Number of curves 88
Conductor 3360033600
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("ey1")
 
E.isogeny_class()
 

Elliptic curves in class 33600ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.dg7 33600ey1 [0,1,0,796033,272996063][0, -1, 0, -796033, -272996063] 13619385906841/604800013619385906841/6048000 2477260800000000024772608000000000 [2][2] 442368442368 2.10432.1043 Γ0(N)\Gamma_0(N)-optimal
33600.dg6 33600ey2 [0,1,0,924033,179172063][0, -1, 0, -924033, -179172063] 21302308926361/893025000021302308926361/8930250000 3657830400000000000036578304000000000000 [2,2][2, 2] 884736884736 2.45082.4508  
33600.dg5 33600ey3 [0,1,0,2356033,1058643937][0, -1, 0, -2356033, 1058643937] 353108405631241/86318776320353108405631241/86318776320 353561707806720000000353561707806720000000 [2][2] 13271041327104 2.65362.6536  
33600.dg8 33600ey4 [0,1,0,3075967,1319172063][0, -1, 0, 3075967, -1319172063] 785793873833639/637994920500785793873833639/637994920500 2613227194368000000000-2613227194368000000000 [2][2] 17694721769472 2.79742.7974  
33600.dg4 33600ey5 [0,1,0,6972033,6963515937][0, -1, 0, -6972033, 6963515937] 9150443179640281/1845703125009150443179640281/184570312500 756000000000000000000756000000000000000000 [2][2] 17694721769472 2.79742.7974  
33600.dg2 33600ey6 [0,1,0,35124033,80127827937][0, -1, 0, -35124033, 80127827937] 1169975873419524361/1084253184001169975873419524361/108425318400 444110104166400000000444110104166400000000 [2,2][2, 2] 26542082654208 3.00013.0001  
33600.dg3 33600ey7 [0,1,0,32564033,92300627937][0, -1, 0, -32564033, 92300627937] 932348627918877961/358766164249920-932348627918877961/358766164249920 1469506208767672320000000-1469506208767672320000000 [2][2] 53084165308416 3.34673.3467  
33600.dg1 33600ey8 [0,1,0,561972033,5127858515937][0, -1, 0, -561972033, 5127858515937] 4791901410190533590281/411600004791901410190533590281/41160000 168591360000000000168591360000000000 [2][2] 53084165308416 3.34673.3467  

Rank

sage: E.rank()
 

The elliptic curves in class 33600ey have rank 11.

Complex multiplication

The elliptic curves in class 33600ey do not have complex multiplication.

Modular form 33600.2.a.ey

sage: E.q_eigenform(10)
 
qq3+q7+q9+2q13+6q17+8q19+O(q20)q - q^{3} + q^{7} + q^{9} + 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1234461212216223663611212244421214631242124161236326612212643122141264123241)\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.