Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("55545.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.v4 55545t1 [1, 0, 1, -12443, -40087] [2] 185856 \(\Gamma_0(N)\)-optimal
55545.v2 55545t2 [1, 0, 1, -142048, -20569519] [2, 2] 371712  
55545.v3 55545t3 [1, 0, 1, -86503, -36810877] [2] 743424  
55545.v1 55545t4 [1, 0, 1, -2271273, -1317693389] [2] 743424  

Rank

sage: E.rank()
 

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

Modular form 55545.2.a.v

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.