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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 28560cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.l4 | 28560cl1 | \([0, -1, 0, 249984, -16257024]\) | \(421792317902132351/271682182840320\) | \(-1112810220913950720\) | \([2]\) | \(430080\) | \(2.1517\) | \(\Gamma_0(N)\)-optimal |
| 28560.l3 | 28560cl2 | \([0, -1, 0, -1060736, -132648960]\) | \(32224493437735955329/16782725759385600\) | \(68742044710443417600\) | \([2, 2]\) | \(860160\) | \(2.4983\) | |
| 28560.l2 | 28560cl3 | \([0, -1, 0, -9590656, 11338387456]\) | \(23818189767728437646209/232359312482640000\) | \(951743743928893440000\) | \([2]\) | \(1720320\) | \(2.8449\) | |
| 28560.l1 | 28560cl4 | \([0, -1, 0, -13502336, -19073740800]\) | \(66464620505913166201729/74880071980801920\) | \(306708774833364664320\) | \([2]\) | \(1720320\) | \(2.8449\) |
Rank
sage: E.rank()
The elliptic curves in class 28560cl have rank \(1\).
Complex multiplication
The elliptic curves in class 28560cl do not have complex multiplication.Modular form 28560.2.a.cl
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.
