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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 28224.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.bn1 | 28224fz4 | \([0, 0, 0, -198156, 31813936]\) | \(306182024/21609\) | \(60729593321521152\) | \([2]\) | \(196608\) | \(1.9678\) | |
| 28224.bn2 | 28224fz2 | \([0, 0, 0, -39396, -2414720]\) | \(19248832/3969\) | \(1394301887483904\) | \([2, 2]\) | \(98304\) | \(1.6212\) | |
| 28224.bn3 | 28224fz1 | \([0, 0, 0, -37191, -2760464]\) | \(1036433728/63\) | \(345808999872\) | \([2]\) | \(49152\) | \(1.2746\) | \(\Gamma_0(N)\)-optimal |
| 28224.bn4 | 28224fz3 | \([0, 0, 0, 84084, -14515760]\) | \(23393656/45927\) | \(-129072517584224256\) | \([2]\) | \(196608\) | \(1.9678\) |
Rank
sage: E.rank()
The elliptic curves in class 28224.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 28224.bn do not have complex multiplication.Modular form 28224.2.a.bn
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.
