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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 365400.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 365400.bk1 | 365400bk3 | \([0, 0, 0, -974475, 370257750]\) | \(8773811642628/203\) | \(2367792000000\) | \([2]\) | \(2883584\) | \(1.8972\) | |
| 365400.bk2 | 365400bk2 | \([0, 0, 0, -60975, 5771250]\) | \(8597884752/41209\) | \(120165444000000\) | \([2, 2]\) | \(1441792\) | \(1.5506\) | |
| 365400.bk3 | 365400bk4 | \([0, 0, 0, -29475, 11724750]\) | \(-242793828/4950967\) | \(-57748079088000000\) | \([2]\) | \(2883584\) | \(1.8972\) | |
| 365400.bk4 | 365400bk1 | \([0, 0, 0, -5850, -16875]\) | \(121485312/69629\) | \(12689885250000\) | \([2]\) | \(720896\) | \(1.2040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 365400.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 365400.bk do not have complex multiplication.Modular form 365400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
