Properties

Label 55470bb
Number of curves $2$
Conductor $55470$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55470.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.y2 55470bb1 [1, 1, 1, 155, -205] [] 24192 \(\Gamma_0(N)\)-optimal
55470.y1 55470bb2 [1, 1, 1, -1780, 33077] [] 72576  

Rank

sage: E.rank()
 

The elliptic curves in class 55470bb have rank \(2\).

Modular form 55470.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - 3q^{11} - q^{12} - 4q^{13} - 2q^{14} - q^{15} + q^{16} - 3q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.