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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 98736k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.j2 | 98736k1 | \([0, -1, 0, -1454944, -674970800]\) | \(187761599684068/10385793\) | \(18840643412861952\) | \([2]\) | \(1382400\) | \(2.1885\) | \(\Gamma_0(N)\)-optimal |
| 98736.j1 | 98736k2 | \([0, -1, 0, -1537224, -594270576]\) | \(110725946217794/21954955473\) | \(79656023803296466944\) | \([2]\) | \(2764800\) | \(2.5350\) |
Rank
sage: E.rank()
The elliptic curves in class 98736k have rank \(0\).
Complex multiplication
The elliptic curves in class 98736k do not have complex multiplication.Modular form 98736.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
