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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 22050bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.a1 | 22050bx1 | \([1, -1, 0, -11780442, -8872398284]\) | \(393349474783/153600000\) | \(70602670807200000000000\) | \([2]\) | \(3010560\) | \(3.0830\) | \(\Gamma_0(N)\)-optimal |
| 22050.a2 | 22050bx2 | \([1, -1, 0, 37611558, -63944478284]\) | \(12801408679457/11250000000\) | \(-5171094053261718750000000\) | \([2]\) | \(6021120\) | \(3.4296\) |
Rank
sage: E.rank()
The elliptic curves in class 22050bx have rank \(1\).
Complex multiplication
The elliptic curves in class 22050bx do not have complex multiplication.Modular form 22050.2.a.bx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
