Properties

Label 8550.y
Number of curves 22
Conductor 85508550
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 8550.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.y1 8550s2 [1,1,1,830,8953][1, -1, 1, -830, -8953] 149721291/722149721291/722 304593750304593750 [2][2] 40964096 0.476530.47653  
8550.y2 8550s1 [1,1,1,80,47][1, -1, 1, -80, 47] 132651/76132651/76 3206250032062500 [2][2] 20482048 0.129960.12996 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8550.y have rank 00.

Complex multiplication

The elliptic curves in class 8550.y do not have complex multiplication.

Modular form 8550.2.a.y

sage: E.q_eigenform(10)
 
q+q2+q4+q82q11+4q13+q16q19+O(q20)q + q^{2} + q^{4} + q^{8} - 2 q^{11} + 4 q^{13} + q^{16} - 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.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.