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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 22218.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22218.y1 | 22218t6 | \([1, 1, 1, -41861897, 104231607419]\) | \(54804145548726848737/637608031452\) | \(94388871769536780828\) | \([2]\) | \(2162688\) | \(2.9837\) | |
| 22218.y2 | 22218t4 | \([1, 1, 1, -9370717, -11044581181]\) | \(614716917569296417/19093020912\) | \(2826452324403510768\) | \([2]\) | \(1081344\) | \(2.6371\) | |
| 22218.y3 | 22218t3 | \([1, 1, 1, -2684157, 1538915331]\) | \(14447092394873377/1439452851984\) | \(213090682617036853776\) | \([2, 2]\) | \(1081344\) | \(2.6371\) | |
| 22218.y4 | 22218t2 | \([1, 1, 1, -610477, -157354909]\) | \(169967019783457/26337394944\) | \(3898879674479145216\) | \([2, 2]\) | \(540672\) | \(2.2906\) | |
| 22218.y5 | 22218t1 | \([1, 1, 1, 66643, -13534621]\) | \(221115865823/664731648\) | \(-98404140458115072\) | \([4]\) | \(270336\) | \(1.9440\) | \(\Gamma_0(N)\)-optimal |
| 22218.y6 | 22218t5 | \([1, 1, 1, 3314703, 7448992203]\) | \(27207619911317663/177609314617308\) | \(-26292552784053884566812\) | \([2]\) | \(2162688\) | \(2.9837\) |
Rank
sage: E.rank()
The elliptic curves in class 22218.y have rank \(1\).
Complex multiplication
The elliptic curves in class 22218.y do not have complex multiplication.Modular form 22218.2.a.y
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
