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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 297024dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
297024.dw1 | 297024dw1 | \([0, -1, 0, -29121, 1921473]\) | \(10418796526321/6390657\) | \(1675272388608\) | \([2]\) | \(1146880\) | \(1.2884\) | \(\Gamma_0(N)\)-optimal |
297024.dw2 | 297024dw2 | \([0, -1, 0, -23681, 2655873]\) | \(-5602762882081/8312741073\) | \(-2179135195840512\) | \([2]\) | \(2293760\) | \(1.6349\) |
Rank
sage: E.rank()
The elliptic curves in class 297024dw have rank \(1\).
Complex multiplication
The elliptic curves in class 297024dw do not have complex multiplication.Modular form 297024.2.a.dw
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.