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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 162450.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.bk1 | 162450du1 | \([1, -1, 0, -2925792, -2217270884]\) | \(-14317849/2700\) | \(-522324173962504687500\) | \([]\) | \(9455616\) | \(2.6995\) | \(\Gamma_0(N)\)-optimal |
| 162450.bk2 | 162450du2 | \([1, -1, 0, 20223333, 10861984741]\) | \(4728305591/3000000\) | \(-580360193291671875000000\) | \([]\) | \(28366848\) | \(3.2488\) |
Rank
sage: E.rank()
The elliptic curves in class 162450.bk have rank \(2\).
Complex multiplication
The elliptic curves in class 162450.bk do not have complex multiplication.Modular form 162450.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
