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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 95550.fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.fy1 | 95550ib2 | \([1, 1, 1, -172628, -27591019]\) | \(38686490446661/141927552\) | \(2087204320656000\) | \([2]\) | \(1032192\) | \(1.8000\) | |
95550.fy2 | 95550ib1 | \([1, 1, 1, -15828, 5781]\) | \(29819839301/17252352\) | \(253715245056000\) | \([2]\) | \(516096\) | \(1.4534\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95550.fy have rank \(2\).
Complex multiplication
The elliptic curves in class 95550.fy do not have complex multiplication.Modular form 95550.2.a.fy
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.