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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 405720.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405720.bu1 | 405720bu2 | \([0, 0, 0, -66003, -6316002]\) | \(9776035692/359375\) | \(1168960464000000\) | \([2]\) | \(1658880\) | \(1.6606\) | \(\Gamma_0(N)\)-optimal* |
405720.bu2 | 405720bu1 | \([0, 0, 0, 1617, -351918]\) | \(574992/66125\) | \(-53772181344000\) | \([2]\) | \(829440\) | \(1.3140\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 405720.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 405720.bu do not have complex multiplication.Modular form 405720.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.