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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 9450.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.bu1 | 9450v2 | \([1, -1, 0, -613242, 184988916]\) | \(268691220631875/7529536\) | \(714717675000000\) | \([3]\) | \(77760\) | \(1.9525\) | |
9450.bu2 | 9450v1 | \([1, -1, 0, -13242, -171084]\) | \(24348886875/12845056\) | \(135475200000000\) | \([]\) | \(25920\) | \(1.4032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.bu do not have complex multiplication.Modular form 9450.2.a.bu
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.