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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 73920.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.cw1 | 73920bg4 | \([0, -1, 0, -19745, -1061343]\) | \(12990838708516/144375\) | \(9461760000\) | \([2]\) | \(98304\) | \(1.0677\) | |
73920.cw2 | 73920bg2 | \([0, -1, 0, -1265, -15375]\) | \(13674725584/1334025\) | \(21856665600\) | \([2, 2]\) | \(49152\) | \(0.72109\) | |
73920.cw3 | 73920bg1 | \([0, -1, 0, -285, 1677]\) | \(2508888064/396165\) | \(405672960\) | \([2]\) | \(24576\) | \(0.37452\) | \(\Gamma_0(N)\)-optimal |
73920.cw4 | 73920bg3 | \([0, -1, 0, 1535, -76415]\) | \(6099383804/41507235\) | \(-2720218152960\) | \([2]\) | \(98304\) | \(1.0677\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.cw have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.cw do not have complex multiplication.Modular form 73920.2.a.cw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.