Properties

Label 6720bi
Number of curves 4
Conductor 6720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6720.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.c4 6720bi1 [0, -1, 0, -1600156, -768989294] [2] 215040 \(\Gamma_0(N)\)-optimal
6720.c2 6720bi2 [0, -1, 0, -25515001, -49598319815] [2, 2] 430080  
6720.c1 6720bi3 [0, -1, 0, -408240001, -3174701034815] [2] 860160  
6720.c3 6720bi4 [0, -1, 0, -25427521, -49955395679] [2] 860160  

Rank

sage: E.rank()
 

The elliptic curves in class 6720bi have rank \(0\).

Modular form 6720.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 6q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.