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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 4998.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4998.bq1 | 4998bm5 | \([1, 0, 0, -672211597, 6708160798793]\) | \(285531136548675601769470657/17941034271597192\) | \(2110744741019138041608\) | \([2]\) | \(1474560\) | \(3.5521\) | |
| 4998.bq2 | 4998bm3 | \([1, 0, 0, -42093157, 104393523905]\) | \(70108386184777836280897/552468975892674624\) | \(64997422544797276838976\) | \([2, 2]\) | \(737280\) | \(3.2055\) | |
| 4998.bq3 | 4998bm6 | \([1, 0, 0, -14337597, 240012741177]\) | \(-2770540998624539614657/209924951154647363208\) | \(-24697460578393107634057992\) | \([2]\) | \(1474560\) | \(3.5521\) | |
| 4998.bq4 | 4998bm2 | \([1, 0, 0, -4445477, -907037055]\) | \(82582985847542515777/44772582831427584\) | \(5267449597534623830016\) | \([2, 2]\) | \(368640\) | \(2.8589\) | |
| 4998.bq5 | 4998bm1 | \([1, 0, 0, -3441957, -2455067007]\) | \(38331145780597164097/55468445663232\) | \(6525807163833581568\) | \([2]\) | \(184320\) | \(2.5124\) | \(\Gamma_0(N)\)-optimal |
| 4998.bq6 | 4998bm4 | \([1, 0, 0, 17145883, -7129667007]\) | \(4738217997934888496063/2928751705237796928\) | \(-344564709369521570782272\) | \([2]\) | \(737280\) | \(3.2055\) |
Rank
sage: E.rank()
The elliptic curves in class 4998.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.bq do not have complex multiplication.Modular form 4998.2.a.bq
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.
