Properties

Label 185130.ec
Number of curves 2
Conductor 185130
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("185130.ec1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 185130.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.ec1 185130bl2 [1, -1, 1, -12806663, 17633175167] [2] 10321920  
185130.ec2 185130bl1 [1, -1, 1, -958343, 159272831] [2] 5160960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185130.ec have rank \(1\).

Modular form 185130.2.a.ec

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.