Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("54720.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54720dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54720.bb3 54720dj1 [0, 0, 0, -17868, 913808] [2] 98304 \(\Gamma_0(N)\)-optimal
54720.bb2 54720dj2 [0, 0, 0, -29388, -408688] [2, 2] 196608  
54720.bb4 54720dj3 [0, 0, 0, 114612, -3231088] [2] 393216  
54720.bb1 54720dj4 [0, 0, 0, -357708, -82226032] [2] 393216  

Rank

sage: E.rank()
 

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

Modular form 54720.2.a.bb

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{11} - 2q^{13} - 2q^{17} - q^{19} + O(q^{20}) \)

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.