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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 127050bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.k2 | 127050bu1 | \([1, 1, 0, 41098041675, -898220963617875]\) | \(2218712073897830722499107/1384711926834951880704\) | \(-4791214151983699587366912000000000\) | \([2]\) | \(1006387200\) | \(5.1518\) | \(\Gamma_0(N)\)-optimal |
127050.k1 | 127050bu2 | \([1, 1, 0, -171397318325, -7327268080417875]\) | \(160934676078320454012702173/86430430219822569086976\) | \(299056209747381035770102128000000000\) | \([2]\) | \(2012774400\) | \(5.4983\) |
Rank
sage: E.rank()
The elliptic curves in class 127050bu have rank \(1\).
Complex multiplication
The elliptic curves in class 127050bu do not have complex multiplication.Modular form 127050.2.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.