Show commands:
SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 154560hn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.bv4 | 154560hn1 | \([0, -1, 0, -4081, -5135]\) | \(458891455696/264449745\) | \(4332744622080\) | \([2]\) | \(245760\) | \(1.1143\) | \(\Gamma_0(N)\)-optimal |
| 154560.bv2 | 154560hn2 | \([0, -1, 0, -46401, -3822399]\) | \(168591300897604/472410225\) | \(30959876505600\) | \([2, 2]\) | \(491520\) | \(1.4609\) | |
| 154560.bv3 | 154560hn3 | \([0, -1, 0, -28001, -6902559]\) | \(-18524646126002/146738831715\) | \(-19233352150548480\) | \([2]\) | \(983040\) | \(1.8075\) | |
| 154560.bv1 | 154560hn4 | \([0, -1, 0, -741921, -245724255]\) | \(344577854816148242/2716875\) | \(356106240000\) | \([2]\) | \(983040\) | \(1.8075\) |
Rank
sage: E.rank()
The elliptic curves in class 154560hn have rank \(0\).
Complex multiplication
The elliptic curves in class 154560hn do not have complex multiplication.Modular form 154560.2.a.hn
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.
