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Properties

Label 54150bj
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 54150bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.z2 54150bj1 \([1, 0, 1, 1484424, -432458702]\) \(3936827539/3158028\) \(-290180096645835937500\) \([2]\) \(2419200\) \(2.6143\) \(\Gamma_0(N)\)-optimal
54150.z1 54150bj2 \([1, 0, 1, -7089326, -3759073702]\) \(428831641421/181752822\) \(16700628193801136718750\) \([2]\) \(4838400\) \(2.9609\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54150.2.a.bj

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