Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("139230.dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139230.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139230.dc1 139230bc3 [1, -1, 1, -6660113, 6617282721] [2] 3932160  
139230.dc2 139230bc4 [1, -1, 1, -810833, -121049823] [2] 3932160  
139230.dc3 139230bc2 [1, -1, 1, -417713, 102714081] [2, 2] 1966080  
139230.dc4 139230bc1 [1, -1, 1, -2993, 4342497] [2] 983040 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 139230.2.a.dc

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.