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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 164934.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164934.bu1 | 164934dv1 | \([1, -1, 0, -86445, -9754907]\) | \(832972004929/610368\) | \(52348895742528\) | \([2]\) | \(1105920\) | \(1.5666\) | \(\Gamma_0(N)\)-optimal |
| 164934.bu2 | 164934dv2 | \([1, -1, 0, -68805, -13865027]\) | \(-420021471169/727634952\) | \(-62406427337061192\) | \([2]\) | \(2211840\) | \(1.9132\) |
Rank
sage: E.rank()
The elliptic curves in class 164934.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 164934.bu do not have complex multiplication.Modular form 164934.2.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.
