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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 705600.bz
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bz1 | \([0, 0, 0, -82670700, 289318054480]\) | \(266916252066900625/162\) | \(37924385587200\) | \([]\) | \(39813120\) | \(2.8282\) |
705600.bz2 | \([0, 0, 0, -1022700, 395175760]\) | \(505318200625/4251528\) | \(995287575350476800\) | \([]\) | \(13271040\) | \(2.2789\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bz do not have complex multiplication.Modular form 705600.2.a.bz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.