Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("106470.eq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106470.eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.eq1 106470ew4 [1, -1, 1, -407153, 100093231] [2] 983040  
106470.eq2 106470ew3 [1, -1, 1, -133373, -17486153] [2] 983040  
106470.eq3 106470ew2 [1, -1, 1, -26903, 1380331] [2, 2] 491520  
106470.eq4 106470ew1 [1, -1, 1, 3517, 127027] [2] 245760 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 106470.2.a.eq

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.