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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 221760.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.bt1 | 221760ml4 | \([0, 0, 0, -55774668, -160325640592]\) | \(100407751863770656369/166028940000\) | \(31728624536125440000\) | \([2]\) | \(15728640\) | \(3.0047\) | |
| 221760.bt2 | 221760ml2 | \([0, 0, 0, -3519948, -2453680528]\) | \(25238585142450289/995844326400\) | \(190308814407755366400\) | \([2, 2]\) | \(7864320\) | \(2.6581\) | |
| 221760.bt3 | 221760ml1 | \([0, 0, 0, -570828, 114413168]\) | \(107639597521009/32699842560\) | \(6249037227947458560\) | \([2]\) | \(3932160\) | \(2.3116\) | \(\Gamma_0(N)\)-optimal |
| 221760.bt4 | 221760ml3 | \([0, 0, 0, 1548852, -8939717008]\) | \(2150235484224911/181905111732960\) | \(-34762608201781173288960\) | \([2]\) | \(15728640\) | \(3.0047\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.bt do not have complex multiplication.Modular form 221760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
