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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 466578cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.cg2 | 466578cg1 | \([1, -1, 0, -3270906, -581485388]\) | \(304821217/164864\) | \(2093189835672542831616\) | \([2]\) | \(24330240\) | \(2.7821\) | \(\Gamma_0(N)\)-optimal |
466578.cg1 | 466578cg2 | \([1, -1, 0, -40597146, -99428834156]\) | \(582810602977/829472\) | \(10531361360727481121568\) | \([2]\) | \(48660480\) | \(3.1287\) |
Rank
sage: E.rank()
The elliptic curves in class 466578cg have rank \(0\).
Complex multiplication
The elliptic curves in class 466578cg do not have complex multiplication.Modular form 466578.2.a.cg
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.