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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 16560.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.bn1 | 16560cb3 | \([0, 0, 0, -1532667, 728720426]\) | \(133345896593725369/340006815000\) | \(1015254909480960000\) | \([4]\) | \(368640\) | \(2.3316\) | |
| 16560.bn2 | 16560cb2 | \([0, 0, 0, -132987, 1726634]\) | \(87109155423289/49979073600\) | \(149236714104422400\) | \([2, 2]\) | \(184320\) | \(1.9850\) | |
| 16560.bn3 | 16560cb1 | \([0, 0, 0, -86907, -9821014]\) | \(24310870577209/114462720\) | \(341783850516480\) | \([2]\) | \(92160\) | \(1.6384\) | \(\Gamma_0(N)\)-optimal |
| 16560.bn4 | 16560cb4 | \([0, 0, 0, 529413, 13782314]\) | \(5495662324535111/3207841648920\) | \(-9578563838208737280\) | \([2]\) | \(368640\) | \(2.3316\) |
Rank
sage: E.rank()
The elliptic curves in class 16560.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.bn do not have complex multiplication.Modular form 16560.2.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.
