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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 83790.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.bs1 | 83790bt2 | \([1, -1, 0, -13239, -573777]\) | \(2992209121/54150\) | \(4644235452150\) | \([2]\) | \(276480\) | \(1.2258\) | |
83790.bs2 | 83790bt1 | \([1, -1, 0, -9, -26055]\) | \(-1/3420\) | \(-293320133820\) | \([2]\) | \(138240\) | \(0.87926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 83790.bs do not have complex multiplication.Modular form 83790.2.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.