Properties

Label 55473.n
Number of curves 4
Conductor 55473
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("55473.n1")
sage: E.isogeny_class()

Elliptic curves in class 55473.n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
55473.n1 55473l4 [1, 0, 1, -246302, 46982081] 2 422400  
55473.n2 55473l2 [1, 0, 1, -19367, 324245] 4 211200  
55473.n3 55473l1 [1, 0, 1, -10962, -438929] 2 105600 \(\Gamma_0(N)\)-optimal
55473.n4 55473l3 [1, 0, 1, 73088, 2543165] 2 422400  

Rank

sage: E.rank()

The elliptic curves in class 55473.n have rank \(0\).

Modular form 55473.2.a.n

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

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 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.