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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 496860.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
496860.bu1 | 496860bu2 | \([0, -1, 0, -12424260, 10668622392]\) | \(4253563312/1476225\) | \(73609691085265728556800\) | \([2]\) | \(63221760\) | \(3.0894\) | \(\Gamma_0(N)\)-optimal* |
496860.bu2 | 496860bu1 | \([0, -1, 0, -5178385, -4411492658]\) | \(4927700992/151875\) | \(473313342883653090000\) | \([2]\) | \(31610880\) | \(2.7428\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 496860.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 496860.bu do not have complex multiplication.Modular form 496860.2.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.