Properties

Label 155526.cp
Number of curves $6$
Conductor $155526$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("155526.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 155526.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
155526.cp1 155526h6 [1, 0, 0, -2051232954, -35757595043640] [2] 103809024  
155526.cp2 155526h3 [1, 0, 0, -459165134, 3786913849620] [2] 51904512  
155526.cp3 155526h4 [1, 0, 0, -131523694, -528242529676] [2, 2] 51904512  
155526.cp4 155526h2 [1, 0, 0, -29913374, 53882993604] [2, 2] 25952256  
155526.cp5 155526h1 [1, 0, 0, 3265506, 4652171460] [2] 12976128 \(\Gamma_0(N)\)-optimal
155526.cp6 155526h5 [1, 0, 0, 162420446, -2554517064352] [2] 103809024  

Rank

sage: E.rank()
 

The elliptic curves in class 155526.cp have rank \(1\).

Modular form 155526.2.a.cp

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.