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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 154560.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.eh1 | 154560bu3 | \([0, 1, 0, -741921, 245724255]\) | \(344577854816148242/2716875\) | \(356106240000\) | \([2]\) | \(983040\) | \(1.8075\) | |
| 154560.eh2 | 154560bu2 | \([0, 1, 0, -46401, 3822399]\) | \(168591300897604/472410225\) | \(30959876505600\) | \([2, 2]\) | \(491520\) | \(1.4609\) | |
| 154560.eh3 | 154560bu4 | \([0, 1, 0, -28001, 6902559]\) | \(-18524646126002/146738831715\) | \(-19233352150548480\) | \([2]\) | \(983040\) | \(1.8075\) | |
| 154560.eh4 | 154560bu1 | \([0, 1, 0, -4081, 5135]\) | \(458891455696/264449745\) | \(4332744622080\) | \([2]\) | \(245760\) | \(1.1143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154560.eh have rank \(2\).
Complex multiplication
The elliptic curves in class 154560.eh do not have complex multiplication.Modular form 154560.2.a.eh
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.
