Properties

Label 6720.f
Number of curves 2
Conductor 6720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6720.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.f1 6720be2 [0, -1, 0, -841, 8041] [2] 4608  
6720.f2 6720be1 [0, -1, 0, 104, 670] [2] 2304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 6720.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} - 2q^{11} + 4q^{13} + q^{15} - 2q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.