Properties

Label 55470.d
Number of curves $4$
Conductor $55470$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55470.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.d1 55470c3 [1, 1, 0, -63431832, 84443489676] [2] 15966720  
55470.d2 55470c1 [1, 1, 0, -32479572, -71256562416] [2] 5322240 \(\Gamma_0(N)\)-optimal
55470.d3 55470c2 [1, 1, 0, -30630572, -79724612616] [2] 10644480  
55470.d4 55470c4 [1, 1, 0, 225474418, 639663520926] [2] 31933440  

Rank

sage: E.rank()
 

The elliptic curves in class 55470.d have rank \(1\).

Modular form 55470.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 2q^{13} + 2q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} - 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.