Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("106470.ff1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106470dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.ff2 106470dn1 [1, -1, 1, -17777, 915581] [2] 221184 \(\Gamma_0(N)\)-optimal
106470.ff3 106470dn2 [1, -1, 1, -12707, 1444889] [2] 442368  
106470.ff1 106470dn3 [1, -1, 1, -71012, -6364601] [2] 663552  
106470.ff4 106470dn4 [1, -1, 1, 111508, -33815609] [2] 1327104  

Rank

sage: E.rank()
 

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

Modular form 106470.2.a.ff

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 Cremona 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 Cremona labels.