Properties

Label 5520.q
Number of curves 44
Conductor 55205520
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 5520.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.q1 5520e3 [0,1,0,2456,47676][0, 1, 0, -2456, -47676] 1600610497636/93151600610497636/9315 95385609538560 [2][2] 35843584 0.529250.52925  
5520.q2 5520e2 [0,1,0,156,756][0, 1, 0, -156, -756] 1650587344/1190251650587344/119025 3047040030470400 [2,2][2, 2] 17921792 0.182670.18267  
5520.q3 5520e1 [0,1,0,31,44][0, 1, 0, -31, 44] 212629504/43125212629504/43125 690000690000 [2][2] 896896 0.16390-0.16390 Γ0(N)\Gamma_0(N)-optimal
5520.q4 5520e4 [0,1,0,144,3036][0, 1, 0, 144, -3036] 320251964/4197615320251964/4197615 4298357760-4298357760 [2][2] 35843584 0.529250.52925  

Rank

sage: E.rank()
 

The elliptic curves in class 5520.q have rank 00.

Complex multiplication

The elliptic curves in class 5520.q do not have complex multiplication.

Modular form 5520.2.a.q

sage: E.q_eigenform(10)
 
q+q3q54q7+q94q11+6q13q152q174q19+O(q20)q + q^{3} - q^{5} - 4 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} - q^{15} - 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 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.