Properties

Label 54720co
Number of curves $4$
Conductor $54720$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54720.eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54720co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54720.eu4 54720co1 [0, 0, 0, -5772, -288016] [2] 147456 \(\Gamma_0(N)\)-optimal
54720.eu3 54720co2 [0, 0, 0, -109452, -13932304] [2, 2] 294912  
54720.eu2 54720co3 [0, 0, 0, -126732, -9239056] [4] 589824  
54720.eu1 54720co4 [0, 0, 0, -1751052, -891859984] [2] 589824  

Rank

sage: E.rank()
 

The elliptic curves in class 54720co have rank \(0\).

Modular form 54720.2.a.eu

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} - 4q^{11} + 2q^{13} + 2q^{17} + q^{19} + O(q^{20}) \)

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.