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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 457776.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.eo1 | 457776eo2 | \([0, 0, 0, -124203819, -531423439270]\) | \(2940001530995593/8673562656\) | \(625141779476406105931776\) | \([2]\) | \(53084160\) | \(3.4360\) | |
457776.eo2 | 457776eo1 | \([0, 0, 0, -11008299, -694924198]\) | \(2046931732873/1181672448\) | \(85168326580306767249408\) | \([2]\) | \(26542080\) | \(3.0894\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 457776.eo do not have complex multiplication.Modular form 457776.2.a.eo
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.