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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 233289.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 233289.bl1 | 233289bl4 | \([1, -1, 0, -28854933, -59638492054]\) | \(209267191953/55223\) | \(701136829722345889887\) | \([2]\) | \(16220160\) | \(2.9844\) | |
| 233289.bl2 | 233289bl2 | \([1, -1, 0, -2026698, -686128465]\) | \(72511713/25921\) | \(329105042522733785049\) | \([2, 2]\) | \(8110080\) | \(2.6378\) | |
| 233289.bl3 | 233289bl1 | \([1, -1, 0, -860253, 299517560]\) | \(5545233/161\) | \(2044130698898967609\) | \([2]\) | \(4055040\) | \(2.2912\) | \(\Gamma_0(N)\)-optimal |
| 233289.bl4 | 233289bl3 | \([1, -1, 0, 6138417, -4829107816]\) | \(2014698447/1958887\) | \(-24870938213503738898703\) | \([2]\) | \(16220160\) | \(2.9844\) |
Rank
sage: E.rank()
The elliptic curves in class 233289.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 233289.bl do not have complex multiplication.Modular form 233289.2.a.bl
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.
