Properties

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

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 54720be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.bt1 54720be1 \([0, 0, 0, -33168, -2168408]\) \(5405726654464/407253125\) \(304012828800000\) \([2]\) \(184320\) \(1.5243\) \(\Gamma_0(N)\)-optimal
54720.bt2 54720be2 \([0, 0, 0, 31812, -9628112]\) \(298091207216/3525390625\) \(-42107040000000000\) \([2]\) \(368640\) \(1.8708\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54720.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} - 6 q^{13} - 2 q^{17} + q^{19} + O(q^{20})\) 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 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.