Properties

Label 106470.bg
Number of curves $4$
Conductor $106470$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106470.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.bg1 106470bu4 [1, -1, 0, -568125, -164679449] [2] 1179648  
106470.bg2 106470bu2 [1, -1, 0, -35775, -2525639] [2, 2] 589824  
106470.bg3 106470bu1 [1, -1, 0, -5355, 96565] [2] 294912 \(\Gamma_0(N)\)-optimal
106470.bg4 106470bu3 [1, -1, 0, 9855, -8557925] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 106470.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 106470.bg do not have complex multiplication.

Modular form 106470.2.a.bg

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 4q^{11} - q^{14} + q^{16} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.