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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 485520.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.bo1 | 485520bo2 | \([0, -1, 0, -971136, 180277440]\) | \(208527857/91875\) | \(44626989683351040000\) | \([2]\) | \(13369344\) | \(2.4662\) | \(\Gamma_0(N)\)-optimal* |
485520.bo2 | 485520bo1 | \([0, -1, 0, 207984, 20860416]\) | \(2048383/1575\) | \(-765034108857446400\) | \([2]\) | \(6684672\) | \(2.1196\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 485520.bo do not have complex multiplication.Modular form 485520.2.a.bo
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.