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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 54150bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.by3 | 54150bu1 | \([1, 1, 1, -279963, -56791719]\) | \(3301293169/22800\) | \(16760095106250000\) | \([2]\) | \(552960\) | \(1.9467\) | \(\Gamma_0(N)\)-optimal |
54150.by2 | 54150bu2 | \([1, 1, 1, -460463, 25155281]\) | \(14688124849/8122500\) | \(5970783881601562500\) | \([2, 2]\) | \(1105920\) | \(2.2933\) | |
54150.by4 | 54150bu3 | \([1, 1, 1, 1795787, 201142781]\) | \(871257511151/527800050\) | \(-387981536626469531250\) | \([2]\) | \(2211840\) | \(2.6399\) | |
54150.by1 | 54150bu4 | \([1, 1, 1, -5604713, 5097385781]\) | \(26487576322129/44531250\) | \(32734560754394531250\) | \([2]\) | \(2211840\) | \(2.6399\) |
Rank
sage: E.rank()
The elliptic curves in class 54150bu have rank \(1\).
Complex multiplication
The elliptic curves in class 54150bu do not have complex multiplication.Modular form 54150.2.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.