Properties

Label 6720.b
Number of curves 6
Conductor 6720
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6720.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.b1 6720e4 [0, -1, 0, -26881, 1705345] [2] 8192  
6720.b2 6720e5 [0, -1, 0, -25921, -1592255] [2] 16384  
6720.b3 6720e3 [0, -1, 0, -2401, 2401] [2, 2] 8192  
6720.b4 6720e2 [0, -1, 0, -1681, 27025] [2, 2] 4096  
6720.b5 6720e1 [0, -1, 0, -61, 781] [2] 2048 \(\Gamma_0(N)\)-optimal
6720.b6 6720e6 [0, -1, 0, 9599, 9601] [2] 16384  

Rank

sage: E.rank()
 

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

Modular form 6720.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.