Properties

Label 6720bx
Number of curves 4
Conductor 6720
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6720.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.bk3 6720bx1 [0, 1, 0, -161, -801] [2] 2048 \(\Gamma_0(N)\)-optimal
6720.bk2 6720bx2 [0, 1, 0, -481, 2975] [2, 2] 4096  
6720.bk1 6720bx3 [0, 1, 0, -7201, 232799] [2] 8192  
6720.bk4 6720bx4 [0, 1, 0, 1119, 19935] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 6720bx have rank \(1\).

Modular form 6720.2.a.bk

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} - q^{7} + q^{9} + 6q^{13} - q^{15} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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.