Properties

Label 139230bh
Number of curves 4
Conductor 139230
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("139230.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139230bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139230.dl4 139230bh1 [1, -1, 1, -48848, 38067] [2] 884736 \(\Gamma_0(N)\)-optimal
139230.dl2 139230bh2 [1, -1, 1, -535568, -150261069] [2, 2] 1769472  
139230.dl3 139230bh3 [1, -1, 1, -296888, -285067533] [2] 3538944  
139230.dl1 139230bh4 [1, -1, 1, -8561768, -9640439949] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 139230bh have rank \(1\).

Modular form 139230.2.a.dl

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + 4q^{11} + q^{13} + q^{14} + q^{16} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.