Properties

Label 54720bx
Number of curves $4$
Conductor $54720$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 54720bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.ex4 54720bx1 \([0, 0, 0, -1094412, -460572176]\) \(-758575480593601/40535043840\) \(-7746367510114467840\) \([2]\) \(1474560\) \(2.3834\) \(\Gamma_0(N)\)-optimal
54720.ex3 54720bx2 \([0, 0, 0, -17729292, -28733214224]\) \(3225005357698077121/8526675600\) \(1629473082546585600\) \([2, 2]\) \(2949120\) \(2.7299\)  
54720.ex2 54720bx3 \([0, 0, 0, -17948172, -27987358736]\) \(3345930611358906241/165622259047500\) \(31650906595820175360000\) \([2]\) \(5898240\) \(3.0765\)  
54720.ex1 54720bx4 \([0, 0, 0, -283668492, -1838928160784]\) \(13209596798923694545921/92340\) \(17646448803840\) \([2]\) \(5898240\) \(3.0765\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54720.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} + 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.