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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 46400.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46400.bt1 | 46400bw2 | \([0, 1, 0, -728033, 240476063]\) | \(-10418796526321/82044596\) | \(-336054665216000000\) | \([]\) | \(537600\) | \(2.1916\) | |
| 46400.bt2 | 46400bw1 | \([0, 1, 0, 7967, -451937]\) | \(13651919/29696\) | \(-121634816000000\) | \([]\) | \(107520\) | \(1.3869\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46400.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 46400.bt do not have complex multiplication.Modular form 46400.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
