Properties

Label 55488bl
Number of curves 6
Conductor 55488
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55488.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55488bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55488.cr5 55488bl1 [0, 1, 0, -629249, 177971295] [2] 884736 \(\Gamma_0(N)\)-optimal
55488.cr4 55488bl2 [0, 1, 0, -2108929, -972923809] [2, 2] 1769472  
55488.cr6 55488bl3 [0, 1, 0, 4179711, -5660476065] [2] 3538944  
55488.cr2 55488bl4 [0, 1, 0, -32072449, -69918983329] [2, 2] 3538944  
55488.cr3 55488bl5 [0, 1, 0, -30407809, -77498755105] [2] 7077888  
55488.cr1 55488bl6 [0, 1, 0, -513153409, -4474407604513] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 55488bl have rank \(2\).

Modular form 55488.2.a.cr

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} - 4q^{11} + 2q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.