Properties

Label 54150bu
Number of curves $4$
Conductor $54150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54150.by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.by3 54150bu1 [1, 1, 1, -279963, -56791719] [2] 552960 \(\Gamma_0(N)\)-optimal
54150.by2 54150bu2 [1, 1, 1, -460463, 25155281] [2, 2] 1105920  
54150.by4 54150bu3 [1, 1, 1, 1795787, 201142781] [2] 2211840  
54150.by1 54150bu4 [1, 1, 1, -5604713, 5097385781] [2] 2211840  

Rank

sage: E.rank()
 

The elliptic curves in class 54150bu have rank \(1\).

Modular form 54150.2.a.by

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.