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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 190575.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.bs1 | 190575bf4 | \([1, -1, 1, -57812855, -167349869728]\) | \(1058993490188089/13182390375\) | \(266009920690099974609375\) | \([2]\) | \(26542080\) | \(3.3046\) | |
| 190575.bs2 | 190575bf2 | \([1, -1, 1, -6765980, 2636224022]\) | \(1697509118089/833765625\) | \(16824712474074462890625\) | \([2, 2]\) | \(13271040\) | \(2.9580\) | |
| 190575.bs3 | 190575bf1 | \([1, -1, 1, -5540855, 5017867022]\) | \(932288503609/779625\) | \(15732198677056640625\) | \([2]\) | \(6635520\) | \(2.6114\) | \(\Gamma_0(N)\)-optimal |
| 190575.bs4 | 190575bf3 | \([1, -1, 1, 24678895, 20182464272]\) | \(82375335041831/56396484375\) | \(-1138035205226898193359375\) | \([2]\) | \(26542080\) | \(3.3046\) |
Rank
sage: E.rank()
The elliptic curves in class 190575.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.bs do not have complex multiplication.Modular form 190575.2.a.bs
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.
