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Properties

Label 54150j
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 54150j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.b1 54150j1 \([1, 1, 0, -862075, 307671625]\) \(96386901625/18468\) \(13575677036062500\) \([2]\) \(1036800\) \(2.0962\) \(\Gamma_0(N)\)-optimal
54150.b2 54150j2 \([1, 1, 0, -771825, 374727375]\) \(-69173457625/42633378\) \(-31339450437750281250\) \([2]\) \(2073600\) \(2.4428\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54150j have rank \(0\).

Complex multiplication

The elliptic curves in class 54150j do not have complex multiplication.

Modular form 54150.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} + 4 q^{11} - q^{12} + 4 q^{14} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.