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Properties

Label 155526ce
Number of curves $2$
Conductor $155526$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 155526ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.bd2 155526ce1 \([1, 0, 1, -39422, 6512636]\) \(-389017/828\) \(-14420675124507708\) \([2]\) \(1520640\) \(1.7896\) \(\Gamma_0(N)\)-optimal
155526.bd1 155526ce2 \([1, 0, 1, -817052, 283971020]\) \(3463512697/3174\) \(55279254643946214\) \([2]\) \(3041280\) \(2.1362\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526ce have rank \(0\).

Complex multiplication

The elliptic curves in class 155526ce do not have complex multiplication.

Modular form 155526.2.a.ce

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.