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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 6160d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6160.f4 | 6160d1 | \([0, 0, 0, -47, -306]\) | \(-44851536/132055\) | \(-33806080\) | \([2]\) | \(1024\) | \(0.13159\) | \(\Gamma_0(N)\)-optimal |
| 6160.f3 | 6160d2 | \([0, 0, 0, -1027, -12654]\) | \(116986321764/148225\) | \(151782400\) | \([2, 2]\) | \(2048\) | \(0.47816\) | |
| 6160.f1 | 6160d3 | \([0, 0, 0, -16427, -810374]\) | \(239369344910082/385\) | \(788480\) | \([2]\) | \(4096\) | \(0.82474\) | |
| 6160.f2 | 6160d4 | \([0, 0, 0, -1307, -5206]\) | \(120564797922/64054375\) | \(131183360000\) | \([4]\) | \(4096\) | \(0.82474\) |
Rank
sage: E.rank()
The elliptic curves in class 6160d have rank \(1\).
Complex multiplication
The elliptic curves in class 6160d do not have complex multiplication.Modular form 6160.2.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.
