Properties

Label 203280.dy
Number of curves 4
Conductor 203280
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.dy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dy1 203280bu3 [0, 1, 0, -63870616, 196447891220] [2] 17694720  
203280.dy2 203280bu2 [0, 1, 0, -4106296, 2883211604] [2, 2] 8847360  
203280.dy3 203280bu1 [0, 1, 0, -969976, -319598380] [2] 4423680 \(\Gamma_0(N)\)-optimal
203280.dy4 203280bu4 [0, 1, 0, 5476904, 14348552084] [2] 17694720  

Rank

sage: E.rank()
 

The elliptic curves in class 203280.dy have rank \(0\).

Modular form 203280.2.a.dy

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.