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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 350658.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.du1 | 350658du2 | \([1, -1, 1, -739454, 196188963]\) | \(26013270347/5398974\) | \(9280533243983325786\) | \([2]\) | \(7096320\) | \(2.3546\) | |
350658.du2 | 350658du1 | \([1, -1, 1, 99076, 18420603]\) | \(62570773/121716\) | \(-209222971684004124\) | \([2]\) | \(3548160\) | \(2.0081\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.du have rank \(1\).
Complex multiplication
The elliptic curves in class 350658.du do not have complex multiplication.Modular form 350658.2.a.du
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.