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("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.f1 6720be2 \([0, -1, 0, -841, 8041]\) \(16079333824/2953125\) \(12096000000\) \([2]\) \(4608\) \(0.65316\)  
6720.f2 6720be1 \([0, -1, 0, 104, 670]\) \(1925134784/4465125\) \(-285768000\) \([2]\) \(2304\) \(0.30659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6720.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.