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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 169065.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169065.y1 | 169065bd1 | \([1, -1, 0, -763830, -234610425]\) | \(13760679326649137/1313522861625\) | \(4704483270170282625\) | \([2]\) | \(3870720\) | \(2.3207\) | \(\Gamma_0(N)\)-optimal |
| 169065.y2 | 169065bd2 | \([1, -1, 0, 909225, -1120994964]\) | \(23209364902764223/164941113796875\) | \(-590749299529270171875\) | \([2]\) | \(7741440\) | \(2.6673\) |
Rank
sage: E.rank()
The elliptic curves in class 169065.y have rank \(1\).
Complex multiplication
The elliptic curves in class 169065.y do not have complex multiplication.Modular form 169065.2.a.y
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.
