Properties

Label 2160.a
Number of curves $2$
Conductor $2160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 2160.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2160.a1 2160n1 \([0, 0, 0, -243, -1998]\) \(-19683/10\) \(-806215680\) \([]\) \(864\) \(0.41377\) \(\Gamma_0(N)\)-optimal
2160.a2 2160n2 \([0, 0, 0, 1917, 25218]\) \(1073733/1000\) \(-725594112000\) \([]\) \(2592\) \(0.96308\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2160.a have rank \(0\).

Complex multiplication

The elliptic curves in class 2160.a do not have complex multiplication.

Modular form 2160.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 3 q^{11} - q^{13} + 3 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.