Properties

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

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

Elliptic curves in class 106470.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.fi1 106470fh6 \([1, -1, 1, -25552832, 49723588581]\) \(524388516989299201/3150\) \(11084042847150\) \([2]\) \(4718592\) \(2.5685\)  
106470.fi2 106470fh4 \([1, -1, 1, -1597082, 777200181]\) \(128031684631201/9922500\) \(34914734968522500\) \([2, 2]\) \(2359296\) \(2.2220\)  
106470.fi3 106470fh5 \([1, -1, 1, -1490612, 885203349]\) \(-104094944089921/35880468750\) \(-126254175555817968750\) \([2]\) \(4718592\) \(2.5685\)  
106470.fi4 106470fh3 \([1, -1, 1, -562802, -153457131]\) \(5602762882081/345888060\) \(1217091453129393660\) \([2]\) \(2359296\) \(2.2220\)  
106470.fi5 106470fh2 \([1, -1, 1, -106502, 10445829]\) \(37966934881/8643600\) \(30414613572579600\) \([2, 2]\) \(1179648\) \(1.8754\)  
106470.fi6 106470fh1 \([1, -1, 1, 15178, 1003461]\) \(109902239/188160\) \(-662086826069760\) \([2]\) \(589824\) \(1.5288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 106470.2.a.fi

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.