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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 160080bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160080.g2 | 160080bs1 | \([0, -1, 0, 751584, 2042023680]\) | \(11462933280746326751/446531557529664000\) | \(-1828993259641503744000\) | \([]\) | \(6967296\) | \(2.7597\) | \(\Gamma_0(N)\)-optimal |
160080.g1 | 160080bs2 | \([0, -1, 0, -101425056, 393313049856]\) | \(-28170823130543688074651809/10140195095015625000\) | \(-41534239109184000000000\) | \([]\) | \(20901888\) | \(3.3090\) |
Rank
sage: E.rank()
The elliptic curves in class 160080bs have rank \(1\).
Complex multiplication
The elliptic curves in class 160080bs do not have complex multiplication.Modular form 160080.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.