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Properties

Label 54450.bi
Number of curves $2$
Conductor $54450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 54450.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54450.bi1 54450bw2 \([1, -1, 0, -5022, -135734]\) \(6352571665/2\) \(4410450\) \([]\) \(41472\) \(0.63650\)  
54450.bi2 54450bw1 \([1, -1, 0, -72, -104]\) \(18865/8\) \(17641800\) \([]\) \(13824\) \(0.087198\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54450.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 54450.bi do not have complex multiplication.

Modular form 54450.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.