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Properties

Label 64974.bw
Number of curves 2
Conductor 64974
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("64974.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64974.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
64974.bw1 64974bx2 [1, 0, 0, -87674406, 422770263012] [7] 14620032  
64974.bw2 64974bx1 [1, 0, 0, -2226316, -1477144936] [] 2088576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 64974.bw have rank \(1\).

Modular form 64974.2.a.bw

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 2q^{11} + q^{12} - q^{13} - q^{15} + q^{16} + q^{17} + q^{18} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.