Properties

Label 54720.bm
Number of curves $2$
Conductor $54720$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 54720.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.bm1 54720bg2 \([0, 0, 0, -932268, -346461392]\) \(468898230633769/5540400\) \(1058786928230400\) \([2]\) \(589824\) \(2.0330\)  
54720.bm2 54720bg1 \([0, 0, 0, -56748, -5709008]\) \(-105756712489/12476160\) \(-2384231305052160\) \([2]\) \(294912\) \(1.6864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54720.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 54720.bm do not have complex multiplication.

Modular form 54720.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} - 6 q^{11} - 2 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.