Properties

Label 5544.f
Number of curves $2$
Conductor $5544$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5544.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5544.f1 5544n1 \([0, 0, 0, -531, -4706]\) \(598885164/539\) \(14902272\) \([2]\) \(1792\) \(0.30083\) \(\Gamma_0(N)\)-optimal
5544.f2 5544n2 \([0, 0, 0, -411, -6890]\) \(-138853062/290521\) \(-16064649216\) \([2]\) \(3584\) \(0.64740\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5544.f have rank \(0\).

Complex multiplication

The elliptic curves in class 5544.f do not have complex multiplication.

Modular form 5544.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} + q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.