Properties

Label 6240.v
Number of curves $4$
Conductor $6240$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6240.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.v1 6240l2 \([0, 1, 0, -25625841, -49938972705]\) \(454357982636417669333824/3003024375\) \(12300387840000\) \([2]\) \(215040\) \(2.5707\)  
6240.v2 6240l3 \([0, 1, 0, -1711496, -667563336]\) \(1082883335268084577352/251301565117746585\) \(128666401340286251520\) \([2]\) \(215040\) \(2.5707\)  
6240.v3 6240l1 \([0, 1, 0, -1601646, -780664896]\) \(7099759044484031233216/577161945398025\) \(36938364505473600\) \([2, 2]\) \(107520\) \(2.2241\) \(\Gamma_0(N)\)-optimal
6240.v4 6240l4 \([0, 1, 0, -1492296, -891720756]\) \(-717825640026599866952/254764560814329735\) \(-130439455136936824320\) \([2]\) \(215040\) \(2.5707\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6240.v have rank \(1\).

Complex multiplication

The elliptic curves in class 6240.v do not have complex multiplication.

Modular form 6240.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.