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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 25350bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25350.bv2 | 25350bu1 | \([1, 0, 1, -54591, -83822]\) | \(29819839301/17252352\) | \(10409225988096000\) | \([2]\) | \(301056\) | \(1.7629\) | \(\Gamma_0(N)\)-optimal |
25350.bv1 | 25350bu2 | \([1, 0, 1, -595391, 176216978]\) | \(38686490446661/141927552\) | \(85632148167696000\) | \([2]\) | \(602112\) | \(2.1095\) |
Rank
sage: E.rank()
The elliptic curves in class 25350bu have rank \(1\).
Complex multiplication
The elliptic curves in class 25350bu do not have complex multiplication.Modular form 25350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.