Properties

Label 208725.y
Number of curves 2
Conductor 208725
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("208725.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 208725.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
208725.y1 208725p2 [1, 0, 0, -3745013, 2767499142] [2] 5529600  
208725.y2 208725p1 [1, 0, 0, -69638, 102852267] [2] 2764800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 208725.y have rank \(1\).

Modular form 208725.2.a.y

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{6} - 2q^{7} + 3q^{8} + q^{9} - q^{12} + 2q^{13} + 2q^{14} - q^{16} - q^{18} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.