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SageMath
E = EllipticCurve("bfs1")
E.isogeny_class()
Elliptic curves in class 705600.bfs
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bfs1 | \([0, 0, 0, -949620, -356171200]\) | \(2156689088/81\) | \(3556892570112000\) | \([2]\) | \(7077888\) | \(2.0704\) |
705600.bfs2 | \([0, 0, 0, -56595, -6105400]\) | \(-29218112/6561\) | \(-4501692159048000\) | \([2]\) | \(3538944\) | \(1.7238\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bfs have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bfs do not have complex multiplication.Modular form 705600.2.a.bfs
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.