Properties

Label 90354k
Number of curves 4
Conductor 90354
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.k3 90354k1 [1, 0, 1, -61634, 4287764] [2] 1036800 \(\Gamma_0(N)\)-optimal
90354.k4 90354k2 [1, 0, 1, 157406, 27944084] [2] 2073600  
90354.k1 90354k3 [1, 0, 1, -13779014, -19687955836] [2] 5184000  
90354.k2 90354k4 [1, 0, 1, -13765324, -19729025836] [2] 10368000  

Rank

sage: E.rank()
 

The elliptic curves in class 90354k have rank \(1\).

Modular form 90354.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + 4q^{5} - q^{6} - 2q^{7} - q^{8} + q^{9} - 4q^{10} + q^{11} + q^{12} - 4q^{13} + 2q^{14} + 4q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.