Properties

Label 6720.bv
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 6720.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bv1 6720cc3 \([0, 1, 0, -4481, -116961]\) \(303735479048/105\) \(3440640\) \([2]\) \(6144\) \(0.61016\)  
6720.bv2 6720cc2 \([0, 1, 0, -281, -1881]\) \(601211584/11025\) \(45158400\) \([2, 2]\) \(3072\) \(0.26359\)  
6720.bv3 6720cc1 \([0, 1, 0, -36, 30]\) \(82881856/36015\) \(2304960\) \([2]\) \(1536\) \(-0.082988\) \(\Gamma_0(N)\)-optimal
6720.bv4 6720cc4 \([0, 1, 0, -1, -5185]\) \(-8/354375\) \(-11612160000\) \([2]\) \(6144\) \(0.61016\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6720.2.a.bv

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.