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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 142800.dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142800.dx1 | 142800eb2 | \([0, -1, 0, -152608, -22892288]\) | \(6141556990297/1019592\) | \(65253888000000\) | \([2]\) | \(589824\) | \(1.6588\) | |
142800.dx2 | 142800eb1 | \([0, -1, 0, -8608, -428288]\) | \(-1102302937/616896\) | \(-39481344000000\) | \([2]\) | \(294912\) | \(1.3122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.dx have rank \(1\).
Complex multiplication
The elliptic curves in class 142800.dx do not have complex multiplication.Modular form 142800.2.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 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.