Properties

Label 208.d
Number of curves 22
Conductor 208208
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 208.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208.d1 208d2 [0,0,0,3403,83834][0, 0, 0, -3403, 83834] 1064019559329/125497034-1064019559329/125497034 514035851264-514035851264 [][] 336336 0.982940.98294  
208.d2 208d1 [0,0,0,43,166][0, 0, 0, -43, -166] 2146689/1664-2146689/1664 6815744-6815744 [][] 4848 0.00998660.0099866 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 208.d have rank 00.

Complex multiplication

The elliptic curves in class 208.d do not have complex multiplication.

Modular form 208.2.a.d

sage: E.q_eigenform(10)
 
q+3q3q5q7+6q9+2q11q133q153q176q19+O(q20)q + 3 q^{3} - q^{5} - q^{7} + 6 q^{9} + 2 q^{11} - q^{13} - 3 q^{15} - 3 q^{17} - 6 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.

(1771)\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.