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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 10890bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10890.be2 | 10890bu1 | \([1, -1, 1, 10867, -1762923]\) | \(109902239/1100000\) | \(-1420614765900000\) | \([]\) | \(72000\) | \(1.5886\) | \(\Gamma_0(N)\)-optimal |
10890.be1 | 10890bu2 | \([1, -1, 1, -6468683, -6330834903]\) | \(-23178622194826561/1610510\) | \(-2079922078754190\) | \([]\) | \(360000\) | \(2.3933\) |
Rank
sage: E.rank()
The elliptic curves in class 10890bu have rank \(0\).
Complex multiplication
The elliptic curves in class 10890bu do not have complex multiplication.Modular form 10890.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.