Properties

Label 5440.k
Number of curves $2$
Conductor $5440$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 5440.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5440.k1 5440e2 \([0, -1, 0, -425025, -109949375]\) \(-32391289681150609/1228250000000\) \(-321978368000000000\) \([]\) \(48384\) \(2.1295\)  
5440.k2 5440e1 \([0, -1, 0, 25535, -496063]\) \(7023836099951/4456448000\) \(-1168231104512000\) \([]\) \(16128\) \(1.5802\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5440.k have rank \(0\).

Complex multiplication

The elliptic curves in class 5440.k do not have complex multiplication.

Modular form 5440.2.a.k

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