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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 8550.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.y1 | 8550s2 | \([1, -1, 1, -830, -8953]\) | \(149721291/722\) | \(304593750\) | \([2]\) | \(4096\) | \(0.47653\) | |
| 8550.y2 | 8550s1 | \([1, -1, 1, -80, 47]\) | \(132651/76\) | \(32062500\) | \([2]\) | \(2048\) | \(0.12996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.y have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.y do not have complex multiplication.Modular form 8550.2.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.
