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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 86640.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86640.bk1 | 86640cg2 | \([0, -1, 0, -10760, 260592]\) | \(4904335099/1822500\) | \(51202160640000\) | \([2]\) | \(184320\) | \(1.3305\) | |
86640.bk2 | 86640cg1 | \([0, -1, 0, -4680, -118800]\) | \(403583419/10800\) | \(303420211200\) | \([2]\) | \(92160\) | \(0.98392\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86640.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 86640.bk do not have complex multiplication.Modular form 86640.2.a.bk
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.