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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 28560.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.e1 | 28560cf4 | \([0, -1, 0, -26976, -1696320]\) | \(530044731605089/26309115\) | \(107762135040\) | \([2]\) | \(65536\) | \(1.1883\) | |
| 28560.e2 | 28560cf3 | \([0, -1, 0, -8576, 287040]\) | \(17032120495489/1339001685\) | \(5484550901760\) | \([2]\) | \(65536\) | \(1.1883\) | |
| 28560.e3 | 28560cf2 | \([0, -1, 0, -1776, -23040]\) | \(151334226289/28676025\) | \(117456998400\) | \([2, 2]\) | \(32768\) | \(0.84172\) | |
| 28560.e4 | 28560cf1 | \([0, -1, 0, 224, -2240]\) | \(302111711/669375\) | \(-2741760000\) | \([2]\) | \(16384\) | \(0.49515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28560.e have rank \(2\).
Complex multiplication
The elliptic curves in class 28560.e do not have complex multiplication.Modular form 28560.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
