Properties

Label 106470fh
Number of curves $6$
Conductor $106470$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("106470.fi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106470fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.fi6 106470fh1 [1, -1, 1, 15178, 1003461] [2] 589824 \(\Gamma_0(N)\)-optimal
106470.fi5 106470fh2 [1, -1, 1, -106502, 10445829] [2, 2] 1179648  
106470.fi4 106470fh3 [1, -1, 1, -562802, -153457131] [2] 2359296  
106470.fi2 106470fh4 [1, -1, 1, -1597082, 777200181] [2, 2] 2359296  
106470.fi3 106470fh5 [1, -1, 1, -1490612, 885203349] [2] 4718592  
106470.fi1 106470fh6 [1, -1, 1, -25552832, 49723588581] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 106470fh have rank \(0\).

Modular form 106470.2.a.fi

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.