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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 7650.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7650.bk1 | 7650cp2 | \([1, -1, 1, -366305, -1824303]\) | \(19088138515945/11040808032\) | \(3144042599737500000\) | \([]\) | \(144000\) | \(2.2388\) | |
| 7650.bk2 | 7650cp1 | \([1, -1, 1, -248630, 47779647]\) | \(3730569358698025/102\) | \(46473750\) | \([]\) | \(28800\) | \(1.4341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7650.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 7650.bk do not have complex multiplication.Modular form 7650.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
