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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 | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16184.d4 | 16184d1 | \([0, 0, 0, 289, 9826]\) | \(432/7\) | \(-43254523648\) | \([2]\) | \(9216\) | \(0.72143\) | \(\Gamma_0(N)\)-optimal |
| 16184.d3 | 16184d2 | \([0, 0, 0, -5491, 147390]\) | \(740772/49\) | \(1211126662144\) | \([2, 2]\) | \(18432\) | \(1.0680\) | |
| 16184.d2 | 16184d3 | \([0, 0, 0, -17051, -677994]\) | \(11090466/2401\) | \(118690412890112\) | \([2]\) | \(36864\) | \(1.4146\) | |
| 16184.d1 | 16184d4 | \([0, 0, 0, -86411, 9776870]\) | \(1443468546/7\) | \(346036189184\) | \([2]\) | \(36864\) | \(1.4146\) |
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.
