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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 96600.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.bx1 | 96600bi1 | \([0, 1, 0, -549708, 139997088]\) | \(36740974400912/4284085869\) | \(2142042934500000000\) | \([2]\) | \(1792000\) | \(2.2490\) | \(\Gamma_0(N)\)-optimal |
96600.bx2 | 96600bi2 | \([0, 1, 0, 772792, 711317088]\) | \(25520019813292/123979339449\) | \(-247958678898000000000\) | \([2]\) | \(3584000\) | \(2.5956\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.bx do not have complex multiplication.Modular form 96600.2.a.bx
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.