Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.c1 6720bi3 \([0, -1, 0, -408240001, -3174701034815]\) \(229625675762164624948320008/9568125\) \(313528320000\) \([2]\) \(860160\) \(3.1066\)  
6720.c2 6720bi2 \([0, -1, 0, -25515001, -49598319815]\) \(448487713888272974160064/91549016015625\) \(374984769600000000\) \([2, 2]\) \(430080\) \(2.7600\)  
6720.c3 6720bi4 \([0, -1, 0, -25427521, -49955395679]\) \(-55486311952875723077768/801237030029296875\) \(-26254935000000000000000\) \([2]\) \(860160\) \(3.1066\)  
6720.c4 6720bi1 \([0, -1, 0, -1600156, -768989294]\) \(7079962908642659949376/100085966990454375\) \(6405501887389080000\) \([2]\) \(215040\) \(2.4134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6720.2.a.c

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.