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SageMath
E = EllipticCurve("ly1")
E.isogeny_class()
Elliptic curves in class 221760ly
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.o3 | 221760ly1 | \([0, 0, 0, -13863, 628252]\) | \(6315211203904/1155\) | \(53887680\) | \([2]\) | \(229376\) | \(0.87808\) | \(\Gamma_0(N)\)-optimal |
| 221760.o2 | 221760ly2 | \([0, 0, 0, -13908, 623968]\) | \(99639211456/1334025\) | \(3983377305600\) | \([2, 2]\) | \(458752\) | \(1.2247\) | |
| 221760.o4 | 221760ly3 | \([0, 0, 0, -2028, 1655152]\) | \(-38614472/49520625\) | \(-1182942351360000\) | \([2]\) | \(917504\) | \(1.5712\) | |
| 221760.o1 | 221760ly4 | \([0, 0, 0, -26508, -681392]\) | \(86233722632/41507235\) | \(991519516753920\) | \([2]\) | \(917504\) | \(1.5712\) |
Rank
sage: E.rank()
The elliptic curves in class 221760ly have rank \(2\).
Complex multiplication
The elliptic curves in class 221760ly do not have complex multiplication.Modular form 221760.2.a.ly
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.
