Properties

Label 6160.n
Number of curves $4$
Conductor $6160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 6160.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.n1 6160k4 \([0, -1, 0, -56320, 5135232]\) \(4823468134087681/30382271150\) \(124445782630400\) \([2]\) \(27648\) \(1.5420\)  
6160.n2 6160k2 \([0, -1, 0, -4320, -103168]\) \(2177286259681/105875000\) \(433664000000\) \([2]\) \(9216\) \(0.99266\)  
6160.n3 6160k3 \([0, -1, 0, -1440, 174080]\) \(-80677568161/3131816380\) \(-12827919892480\) \([2]\) \(13824\) \(1.1954\)  
6160.n4 6160k1 \([0, -1, 0, 160, -6400]\) \(109902239/4312000\) \(-17661952000\) \([2]\) \(4608\) \(0.64608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6160.n have rank \(0\).

Complex multiplication

The elliptic curves in class 6160.n do not have complex multiplication.

Modular form 6160.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.