Properties

Label 201840.cv
Number of curves 44
Conductor 201840201840
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 201840.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201840.cv1 201840a3 [0,1,0,3465200,2445222420][0, 1, 0, -3465200, 2445222420] 1888690601881/318276451888690601881/31827645 7754475724189304832077544757241893048320 [2][2] 1032192010321920 2.61442.6144  
201840.cv2 201840a2 [0,1,0,437600,53153100][0, 1, 0, -437600, -53153100] 3803721481/17030253803721481/1703025 41492438476637184004149243847663718400 [2,2][2, 2] 51609605160960 2.26792.2679  
201840.cv3 201840a1 [0,1,0,370320,86820012][0, 1, 0, -370320, -86820012] 2305199161/13052305199161/1305 31794972012748803179497201274880 [2][2] 25804802580480 1.92131.9213 Γ0(N)\Gamma_0(N)-optimal
201840.cv4 201840a4 [0,1,0,1513520,395769772][0, 1, 0, 1513520, -395769772] 157376536199/118918125157376536199/118918125 289731682466173440000-289731682466173440000 [4][4] 1032192010321920 2.61442.6144  

Rank

sage: E.rank()
 

The elliptic curves in class 201840.cv have rank 00.

Complex multiplication

The elliptic curves in class 201840.cv do not have complex multiplication.

Modular form 201840.2.a.cv

sage: E.q_eigenform(10)
 
q+q3+q54q7+q94q11+6q13+q156q174q19+O(q20)q + q^{3} + q^{5} - 4 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} + q^{15} - 6 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 LMFDB numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.