Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.z3 6720bv1 [0, -1, 0, -225, 897] [2] 3072 \(\Gamma_0(N)\)-optimal
6720.z2 6720bv2 [0, -1, 0, -1505, -21375] [2, 2] 6144  
6720.z1 6720bv3 [0, -1, 0, -23905, -1414655] [2] 12288  
6720.z4 6720bv4 [0, -1, 0, 415, -73983] [4] 12288  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 6720bv do not have complex multiplication.

Modular form 6720.2.a.bv

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 6q^{17} + O(q^{20}) \)

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.