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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 110466.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110466.bu1 | 110466bj6 | \([1, -1, 1, -90140324, -329379883419]\) | \(2361739090258884097/5202\) | \(178410118589298\) | \([2]\) | \(7077888\) | \(2.8686\) | |
110466.bu2 | 110466bj4 | \([1, -1, 1, -5633834, -5145382587]\) | \(576615941610337/27060804\) | \(928089436901528196\) | \([2, 2]\) | \(3538944\) | \(2.5220\) | |
110466.bu3 | 110466bj5 | \([1, -1, 1, -5341424, -5703534795]\) | \(-491411892194497/125563633938\) | \(-4306386547747363136562\) | \([2]\) | \(7077888\) | \(2.8686\) | |
110466.bu4 | 110466bj2 | \([1, -1, 1, -370454, -71484267]\) | \(163936758817/30338064\) | \(1040487811612785936\) | \([2, 2]\) | \(1769472\) | \(2.1755\) | |
110466.bu5 | 110466bj1 | \([1, -1, 1, -110534, 13145685]\) | \(4354703137/352512\) | \(12089909212639488\) | \([2]\) | \(884736\) | \(1.8289\) | \(\Gamma_0(N)\)-optimal |
110466.bu6 | 110466bj3 | \([1, -1, 1, 734206, -417021915]\) | \(1276229915423/2927177028\) | \(-100391772529286595972\) | \([2]\) | \(3538944\) | \(2.5220\) |
Rank
sage: E.rank()
The elliptic curves in class 110466.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 110466.bu do not have complex multiplication.Modular form 110466.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.