Properties

Label 55545.g
Number of curves 4
Conductor 55545
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55545.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.g1 55545u4 [1, 0, 0, -24334540, -46206373633] [2] 2230272  
55545.g2 55545u2 [1, 0, 0, -1521415, -721565008] [2, 2] 1115136  
55545.g3 55545u3 [1, 0, 0, -1095570, -1134038475] [4] 2230272  
55545.g4 55545u1 [1, 0, 0, -122210, -4332525] [2] 557568 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55545.g have rank \(0\).

Modular form 55545.2.a.g

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

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.