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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 226576.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226576.bu1 | 226576bf1 | \([0, 0, 0, -595595, 167128122]\) | \(9869198625/614656\) | \(1455214714774618112\) | \([2]\) | \(2359296\) | \(2.2366\) | \(\Gamma_0(N)\)-optimal |
226576.bu2 | 226576bf2 | \([0, 0, 0, 470645, 700034874]\) | \(4869777375/92236816\) | \(-218373158135866130432\) | \([2]\) | \(4718592\) | \(2.5831\) |
Rank
sage: E.rank()
The elliptic curves in class 226576.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 226576.bu do not have complex multiplication.Modular form 226576.2.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.