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Properties

Label 139650.cw
Number of curves $2$
Conductor $139650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.cw1 139650fm2 \([1, 0, 1, -45726826, -124572092452]\) \(-46017030564782549/2542728609792\) \(-584276324635584000000000\) \([]\) \(28800000\) \(3.3182\)  
139650.cw2 139650fm1 \([1, 0, 1, 241299, 468190048]\) \(6761990971/415984632\) \(-95586281191734375000\) \([]\) \(5760000\) \(2.5135\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139650.cw have rank \(1\).

Complex multiplication

The elliptic curves in class 139650.cw do not have complex multiplication.

Modular form 139650.2.a.cw

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 3 q^{11} + q^{12} - q^{13} + q^{16} - 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.