Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("106470.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106470.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.l1 106470a3 [1, -1, 0, -159990, -24560704] [2] 663552  
106470.l2 106470a4 [1, -1, 0, -114360, -38897650] [2] 1327104  
106470.l3 106470a1 [1, -1, 0, -7890, 238356] [2] 221184 \(\Gamma_0(N)\)-optimal
106470.l4 106470a2 [1, -1, 0, 12390, 1248300] [2] 442368  

Rank

sage: E.rank()
 

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

Modular form 106470.2.a.l

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.