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SageMath
E = EllipticCurve("f1")
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)
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.