Properties

Label 2160.s
Number of curves $2$
Conductor $2160$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2160.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2160.s1 2160p1 \([0, 0, 0, -72, 236]\) \(-5971968/25\) \(-172800\) \([]\) \(288\) \(-0.14004\) \(\Gamma_0(N)\)-optimal
2160.s2 2160p2 \([0, 0, 0, 168, 1244]\) \(8429568/15625\) \(-972000000\) \([]\) \(864\) \(0.40927\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2160.s have rank \(1\).

Complex multiplication

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

Modular form 2160.2.a.s

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