Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("55545.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.f1 55545m4 [1, 0, 0, -2343481, 1376328380] [2] 1081344  
55545.f2 55545m2 [1, 0, 0, -214256, -428505] [2, 2] 540672  
55545.f3 55545m1 [1, 0, 0, -148131, -21892680] [2] 270336 \(\Gamma_0(N)\)-optimal
55545.f4 55545m3 [1, 0, 0, 856969, -3213690] [2] 1081344  

Rank

sage: E.rank()
 

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

Modular form 55545.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{7} + 3q^{8} + q^{9} + q^{10} - q^{12} + 2q^{13} - q^{14} - q^{15} - q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.