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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 360672.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360672.bk1 | 360672bk2 | \([0, 1, 0, -379553, -90077361]\) | \(61162984000/41067\) | \(4060190908919808\) | \([2]\) | \(2949120\) | \(1.9334\) | |
360672.bk2 | 360672bk1 | \([0, 1, 0, -28418, -818844]\) | \(1643032000/767637\) | \(1185849027484992\) | \([2]\) | \(1474560\) | \(1.5868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 360672.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 360672.bk do not have complex multiplication.Modular form 360672.2.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.