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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 14490bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bo3 | 14490bp1 | \([1, -1, 1, -1981823, -1073358169]\) | \(1180838681727016392361/692428800000\) | \(504780595200000\) | \([2]\) | \(245760\) | \(2.1454\) | \(\Gamma_0(N)\)-optimal |
| 14490.bo2 | 14490bp2 | \([1, -1, 1, -1993343, -1060239193]\) | \(1201550658189465626281/28577902500000000\) | \(20833290922500000000\) | \([2, 2]\) | \(491520\) | \(2.4920\) | |
| 14490.bo1 | 14490bp3 | \([1, -1, 1, -4427663, 2039137031]\) | \(13167998447866683762601/5158996582031250000\) | \(3760908508300781250000\) | \([2]\) | \(983040\) | \(2.8385\) | |
| 14490.bo4 | 14490bp4 | \([1, -1, 1, 256657, -3320139193]\) | \(2564821295690373719/6533572090396050000\) | \(-4762974053898720450000\) | \([2]\) | \(983040\) | \(2.8385\) |
Rank
sage: E.rank()
The elliptic curves in class 14490bp have rank \(0\).
Complex multiplication
The elliptic curves in class 14490bp do not have complex multiplication.Modular form 14490.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
