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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 155526.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.bk1 | 155526cl2 | \([1, 0, 1, -6487106645, 201095334472736]\) | \(1733490909744055732873/99355964553216\) | \(1730410732492791743297304576\) | \([2]\) | \(214106112\) | \(4.2902\) | |
155526.bk2 | 155526cl1 | \([1, 0, 1, -382192725, 3518342331424]\) | \(-354499561600764553/101902222098432\) | \(-1774757052351350235727921152\) | \([2]\) | \(107053056\) | \(3.9436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 155526.bk do not have complex multiplication.Modular form 155526.2.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.