Properties

Label 6720.y
Number of curves $4$
Conductor $6720$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 6720.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.y1 6720n4 \([0, -1, 0, -1505, 22977]\) \(11512557512/2835\) \(92897280\) \([2]\) \(4096\) \(0.51684\)  
6720.y2 6720n3 \([0, -1, 0, -705, -6783]\) \(1184287112/36015\) \(1180139520\) \([2]\) \(4096\) \(0.51684\)  
6720.y3 6720n2 \([0, -1, 0, -105, 297]\) \(31554496/11025\) \(45158400\) \([2, 2]\) \(2048\) \(0.17027\)  
6720.y4 6720n1 \([0, -1, 0, 20, 22]\) \(13144256/13125\) \(-840000\) \([2]\) \(1024\) \(-0.17631\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6720.y have rank \(1\).

Complex multiplication

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

Modular form 6720.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.