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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 43350.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43350.bk1 | 43350ba6 | \([1, 0, 1, -200450551, -1092359612752]\) | \(2361739090258884097/5202\) | \(1961931780281250\) | \([2]\) | \(4718592\) | \(3.0684\) | |
| 43350.bk2 | 43350ba4 | \([1, 0, 1, -12528301, -17068498252]\) | \(576615941610337/27060804\) | \(10205969121023062500\) | \([2, 2]\) | \(2359296\) | \(2.7218\) | |
| 43350.bk3 | 43350ba5 | \([1, 0, 1, -11878051, -18919109752]\) | \(-491411892194497/125563633938\) | \(-47356263719831511281250\) | \([2]\) | \(4718592\) | \(3.0684\) | |
| 43350.bk4 | 43350ba2 | \([1, 0, 1, -823801, -237427252]\) | \(163936758817/30338064\) | \(11441986142600250000\) | \([2, 2]\) | \(1179648\) | \(2.3753\) | |
| 43350.bk5 | 43350ba1 | \([1, 0, 1, -245801, 43480748]\) | \(4354703137/352512\) | \(132949730052000000\) | \([2]\) | \(589824\) | \(2.0287\) | \(\Gamma_0(N)\)-optimal |
| 43350.bk6 | 43350ba3 | \([1, 0, 1, 1632699, -1382156252]\) | \(1276229915423/2927177028\) | \(-1103983398258827062500\) | \([2]\) | \(2359296\) | \(2.7218\) |
Rank
sage: E.rank()
The elliptic curves in class 43350.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 43350.bk do not have complex multiplication.Modular form 43350.2.a.bk
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
