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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 141570dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.n2 | 141570dx1 | \([1, -1, 0, -726930, 320519700]\) | \(-32894113444921/15289560000\) | \(-19745977000103640000\) | \([2]\) | \(3686400\) | \(2.4087\) | \(\Gamma_0(N)\)-optimal |
141570.n1 | 141570dx2 | \([1, -1, 0, -12705930, 17433719100]\) | \(175654575624148921/21954418200\) | \(28353427883330635800\) | \([2]\) | \(7372800\) | \(2.7552\) |
Rank
sage: E.rank()
The elliptic curves in class 141570dx have rank \(1\).
Complex multiplication
The elliptic curves in class 141570dx do not have complex multiplication.Modular form 141570.2.a.dx
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.