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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 248430cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.cu2 | 248430cu1 | \([1, 0, 1, 32951, 6393272]\) | \(6967871/35100\) | \(-19932210746639100\) | \([2]\) | \(2903040\) | \(1.8098\) | \(\Gamma_0(N)\)-optimal |
248430.cu1 | 248430cu2 | \([1, 0, 1, -381099, 81087892]\) | \(10779215329/1232010\) | \(699620597207032410\) | \([2]\) | \(5806080\) | \(2.1564\) |
Rank
sage: E.rank()
The elliptic curves in class 248430cu have rank \(1\).
Complex multiplication
The elliptic curves in class 248430cu do not have complex multiplication.Modular form 248430.2.a.cu
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.