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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 350658.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.bk1 | 350658bk2 | \([1, -1, 0, -259386, 50752862]\) | \(1494447319737/5411854\) | \(6989236093904526\) | \([2]\) | \(3932160\) | \(1.9013\) | |
350658.bk2 | 350658bk1 | \([1, -1, 0, -8916, 1510460]\) | \(-60698457/725788\) | \(-937331954284572\) | \([2]\) | \(1966080\) | \(1.5547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 350658.bk do not have complex multiplication.Modular form 350658.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.