Properties

Label 106470.eq
Number of curves $4$
Conductor $106470$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 106470.eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.eq1 106470ew4 \([1, -1, 1, -407153, 100093231]\) \(2121328796049/120050\) \(422425188508050\) \([2]\) \(983040\) \(1.8708\)  
106470.eq2 106470ew3 \([1, -1, 1, -133373, -17486153]\) \(74565301329/5468750\) \(19243129942968750\) \([2]\) \(983040\) \(1.8708\)  
106470.eq3 106470ew2 \([1, -1, 1, -26903, 1380331]\) \(611960049/122500\) \(431046110722500\) \([2, 2]\) \(491520\) \(1.5242\)  
106470.eq4 106470ew1 \([1, -1, 1, 3517, 127027]\) \(1367631/2800\) \(-9852482530800\) \([2]\) \(245760\) \(1.1776\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 106470.2.a.eq

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.