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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 169050.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.bb1 | 169050il1 | \([1, 1, 0, -6327150, 6118744500]\) | \(15238420194810961/12619514880\) | \(23198020408080000000\) | \([2]\) | \(7741440\) | \(2.6442\) | \(\Gamma_0(N)\)-optimal |
169050.bb2 | 169050il2 | \([1, 1, 0, -4955150, 8847652500]\) | \(-7319577278195281/14169067365600\) | \(-26046509476491787500000\) | \([2]\) | \(15482880\) | \(2.9908\) |
Rank
sage: E.rank()
The elliptic curves in class 169050.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 169050.bb do not have complex multiplication.Modular form 169050.2.a.bb
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.