Properties

Label 382200v
Number of curves 66
Conductor 382200382200
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 382200v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.v5 382200v1 [0,1,0,900783,429604188][0, -1, 0, -900783, -429604188] 2748251600896/1124136195-2748251600896/1124136195 33063374801388750000-33063374801388750000 [2][2] 94371849437184 2.45382.4538 Γ0(N)\Gamma_0(N)-optimal
382200.v4 382200v2 [0,1,0,15606908,23724106188][0, -1, 0, -15606908, -23724106188] 893359210685776/91298025893359210685776/91298025 4296448537290000000042964485372900000000 [2,2][2, 2] 1887436818874368 2.80042.8004  
382200.v3 382200v3 [0,1,0,16807408,19860897188][0, -1, 0, -16807408, -19860897188] 278944461825124/70849130625278944461825124/70849130625 133365269902410000000000133365269902410000000000 [2,2][2, 2] 3774873637748736 3.14693.1469  
382200.v1 382200v4 [0,1,0,249704408,1518670741188][0, -1, 0, -249704408, -1518670741188] 914732517663095044/9555914732517663095044/9555 1798617912000000017986179120000000 [2][2] 3774873637748736 3.14693.1469  
382200.v2 382200v5 [0,1,0,93982408,334372352812][0, -1, 0, -93982408, 334372352812] 24385137179326562/128477588557524385137179326562/1284775885575 48368831411844216000000004836883141184421600000000 [2][2] 7549747275497472 3.49353.4935  
382200.v6 382200v6 [0,1,0,41159592,126867979188][0, -1, 0, 41159592, -126867979188] 2048324060764798/30318996093752048324060764798/3031899609375 11414398628587500000000000-11414398628587500000000000 [2][2] 7549747275497472 3.49353.4935  

Rank

sage: E.rank()
 

The elliptic curves in class 382200v have rank 11.

Complex multiplication

The elliptic curves in class 382200v do not have complex multiplication.

Modular form 382200.2.a.v

sage: E.q_eigenform(10)
 
qq3+q94q11+q13+2q174q19+O(q20)q - q^{3} + q^{9} - 4 q^{11} + q^{13} + 2 q^{17} - 4 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.

(124488212244421422424188842814842841)\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.