Properties

Label 6720q
Number of curves $6$
Conductor $6720$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6720.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.bl4 6720q1 [0, 1, 0, -701, 6915] [2] 2048 \(\Gamma_0(N)\)-optimal
6720.bl3 6720q2 [0, 1, 0, -721, 6479] [2, 2] 4096  
6720.bl2 6720q3 [0, 1, 0, -2721, -48321] [2, 2] 8192  
6720.bl5 6720q4 [0, 1, 0, 959, 33695] [2] 8192  
6720.bl1 6720q5 [0, 1, 0, -41921, -3317601] [2] 16384  
6720.bl6 6720q6 [0, 1, 0, 4479, -254241] [2] 16384  

Rank

sage: E.rank()
 

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

Modular form 6720.2.a.bl

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.