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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 79800bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79800.bm4 | 79800bu1 | \([0, 1, 0, -108983, -5460462]\) | \(572616640141312/280535480757\) | \(70133870189250000\) | \([2]\) | \(786432\) | \(1.9257\) | \(\Gamma_0(N)\)-optimal |
79800.bm2 | 79800bu2 | \([0, 1, 0, -929108, 340632288]\) | \(22174957026242512/278654127129\) | \(1114616508516000000\) | \([2, 2]\) | \(1572864\) | \(2.2723\) | |
79800.bm3 | 79800bu3 | \([0, 1, 0, -159608, 888516288]\) | \(-28104147578308/21301741002339\) | \(-340827856037424000000\) | \([2]\) | \(3145728\) | \(2.6189\) | |
79800.bm1 | 79800bu4 | \([0, 1, 0, -14820608, 21955806288]\) | \(22501000029889239268/3620708343\) | \(57931333488000000\) | \([2]\) | \(3145728\) | \(2.6189\) |
Rank
sage: E.rank()
The elliptic curves in class 79800bu have rank \(1\).
Complex multiplication
The elliptic curves in class 79800bu do not have complex multiplication.Modular form 79800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.