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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 86190.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86190.bw1 | 86190bs4 | \([1, 1, 1, -1250181, -535180131]\) | \(44769506062996441/323730468750\) | \(1562585140136718750\) | \([2]\) | \(3612672\) | \(2.3227\) | |
| 86190.bw2 | 86190bs2 | \([1, 1, 1, -129711, 3990033]\) | \(50002789171321/27473062500\) | \(132607225332562500\) | \([2, 2]\) | \(1806336\) | \(1.9762\) | |
| 86190.bw3 | 86190bs1 | \([1, 1, 1, -99291, 11984409]\) | \(22428153804601/35802000\) | \(172809415818000\) | \([2]\) | \(903168\) | \(1.6296\) | \(\Gamma_0(N)\)-optimal |
| 86190.bw4 | 86190bs3 | \([1, 1, 1, 504039, 32128533]\) | \(2933972022568679/1789082460750\) | \(-8635559323290246750\) | \([2]\) | \(3612672\) | \(2.3227\) |
Rank
sage: E.rank()
The elliptic curves in class 86190.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 86190.bw do not have complex multiplication.Modular form 86190.2.a.bw
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.
