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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 93100.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93100.bs1 | 93100y1 | \([0, -1, 0, -1128633, -430042738]\) | \(5405726654464/407253125\) | \(11978230725781250000\) | \([2]\) | \(2073600\) | \(2.4060\) | \(\Gamma_0(N)\)-optimal |
93100.bs2 | 93100y2 | \([0, -1, 0, 1082492, -1911496488]\) | \(298091207216/3525390625\) | \(-1659034726562500000000\) | \([2]\) | \(4147200\) | \(2.7526\) |
Rank
sage: E.rank()
The elliptic curves in class 93100.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 93100.bs do not have complex multiplication.Modular form 93100.2.a.bs
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.