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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 76050bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.h1 | 76050bu1 | \([1, -1, 0, -31979817, 69606955341]\) | \(65787589563409/10400000\) | \(571795861162500000000\) | \([2]\) | \(7741440\) | \(2.9935\) | \(\Gamma_0(N)\)-optimal |
76050.h2 | 76050bu2 | \([1, -1, 0, -28937817, 83378089341]\) | \(-48743122863889/26406250000\) | \(-1451825428732910156250000\) | \([2]\) | \(15482880\) | \(3.3400\) |
Rank
sage: E.rank()
The elliptic curves in class 76050bu have rank \(0\).
Complex multiplication
The elliptic curves in class 76050bu do not have complex multiplication.Modular form 76050.2.a.bu
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 Cremona 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 Cremona labels.