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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 25872.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.bs1 | 25872cp2 | \([0, 1, 0, -604, -2920]\) | \(810448/363\) | \(10932886272\) | \([2]\) | \(17280\) | \(0.62166\) | |
25872.bs2 | 25872cp1 | \([0, 1, 0, 131, -274]\) | \(131072/99\) | \(-186356016\) | \([2]\) | \(8640\) | \(0.27509\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 25872.bs do not have complex multiplication.Modular form 25872.2.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.