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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 8550.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.x1 | 8550x3 | \([1, -1, 1, -139730, 20109647]\) | \(26487576322129/44531250\) | \(507238769531250\) | \([2]\) | \(49152\) | \(1.7169\) | |
8550.x2 | 8550x2 | \([1, -1, 1, -11480, 102647]\) | \(14688124849/8122500\) | \(92520351562500\) | \([2, 2]\) | \(24576\) | \(1.3704\) | |
8550.x3 | 8550x1 | \([1, -1, 1, -6980, -221353]\) | \(3301293169/22800\) | \(259706250000\) | \([2]\) | \(12288\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
8550.x4 | 8550x4 | \([1, -1, 1, 44770, 777647]\) | \(871257511151/527800050\) | \(-6011972444531250\) | \([2]\) | \(49152\) | \(1.7169\) |
Rank
sage: E.rank()
The elliptic curves in class 8550.x have rank \(1\).
Complex multiplication
The elliptic curves in class 8550.x do not have complex multiplication.Modular form 8550.2.a.x
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.