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SageMath
E = EllipticCurve("ok1")
E.isogeny_class()
Elliptic curves in class 187200.ok
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.ok1 | 187200bu1 | \([0, 0, 0, -5250960300, -146455678711600]\) | \(-134057911417971280740025/1872\) | \(-223590481920000\) | \([]\) | \(51609600\) | \(3.7330\) | \(\Gamma_0(N)\)-optimal |
| 187200.ok2 | 187200bu2 | \([0, 0, 0, -5116363500, -154318995790000]\) | \(-198417696411528597145/22989483914821632\) | \(-1716155778447868900147200000000\) | \([]\) | \(258048000\) | \(4.5378\) |
Rank
sage: E.rank()
The elliptic curves in class 187200.ok have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.ok do not have complex multiplication.Modular form 187200.2.a.ok
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
