Properties

Label 55545.t
Number of curves 4
Conductor 55545
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("55545.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.t1 55545g4 [1, 0, 1, -59524, 5584241] [2] 180224  
55545.t2 55545g2 [1, 0, 1, -3979, 74177] [2, 2] 90112  
55545.t3 55545g1 [1, 0, 1, -1334, -17869] [2] 45056 \(\Gamma_0(N)\)-optimal
55545.t4 55545g3 [1, 0, 1, 9246, 465637] [2] 180224  

Rank

sage: E.rank()
 

The elliptic curves in class 55545.t have rank \(1\).

Modular form 55545.2.a.t

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

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.