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SageMath
sage: E = EllipticCurve("d1")
sage: E.isogeny_class()
Elliptic curves in class 16184d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
16184.d4 | 16184d1 | [0, 0, 0, 289, 9826] | [2] | 9216 | \(\Gamma_0(N)\)-optimal |
16184.d3 | 16184d2 | [0, 0, 0, -5491, 147390] | [2, 2] | 18432 | |
16184.d2 | 16184d3 | [0, 0, 0, -17051, -677994] | [2] | 36864 | |
16184.d1 | 16184d4 | [0, 0, 0, -86411, 9776870] | [2] | 36864 |
Rank
sage: E.rank()
The elliptic curves in class 16184d have rank \(1\).
Complex multiplication
The elliptic curves in class 16184d do not have complex multiplication.Modular form 16184.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.