Properties

Label 55506bd
Number of curves 4
Conductor 55506
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55506.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55506bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55506.ba3 55506bd1 [1, 1, 1, -4643, 112925] [2] 96768 \(\Gamma_0(N)\)-optimal
55506.ba4 55506bd2 [1, 1, 1, 3767, 486329] [2] 193536  
55506.ba1 55506bd3 [1, 1, 1, -67718, -6784957] [2] 290304  
55506.ba2 55506bd4 [1, 1, 1, -34078, -13486045] [2] 580608  

Rank

sage: E.rank()
 

The elliptic curves in class 55506bd have rank \(1\).

Modular form 55506.2.a.ba

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.