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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 141610.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.bu1 | 141610j2 | \([1, 0, 0, -16866046, -26661044124]\) | \(544737993463/20000\) | \(19480759467227660000\) | \([2]\) | \(9318400\) | \(2.7889\) | |
141610.bu2 | 141610j1 | \([1, 0, 0, -1005726, -456623420]\) | \(-115501303/25600\) | \(-24935372118051404800\) | \([2]\) | \(4659200\) | \(2.4424\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141610.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 141610.bu do not have complex multiplication.Modular form 141610.2.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 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.