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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 450800fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.fy2 | 450800fy1 | \([0, -1, 0, 5134792, 659366912]\) | \(7953970437500/4703287687\) | \(-8853393489405808000000\) | \([2]\) | \(26542080\) | \(2.9006\) | \(\Gamma_0(N)\)-optimal* |
450800.fy1 | 450800fy2 | \([0, -1, 0, -20786208, 5325146912]\) | \(263822189935250/149429406721\) | \(562567048682205728000000\) | \([2]\) | \(53084160\) | \(3.2472\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800fy have rank \(1\).
Complex multiplication
The elliptic curves in class 450800fy do not have complex multiplication.Modular form 450800.2.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 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.