Properties

Label 54150.k
Number of curves $2$
Conductor $54150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54150.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.k1 54150c2 [1, 1, 0, -644525, 198868125] [2] 491520  
54150.k2 54150c1 [1, 1, 0, -36525, 3700125] [2] 245760 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 54150.2.a.k

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.