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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 259182.fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.fh1 | 259182fh6 | \([1, -1, 1, -14939559779, -702833547127269]\) | \(285531136548675601769470657/17941034271597192\) | \(23170271092499019938343048\) | \([2]\) | \(314572800\) | \(4.3274\) | |
| 259182.fh2 | 259182fh4 | \([1, -1, 1, -935498939, -10937714017557]\) | \(70108386184777836280897/552468975892674624\) | \(713495986231622458635118656\) | \([2, 2]\) | \(157286400\) | \(3.9808\) | |
| 259182.fh3 | 259182fh5 | \([1, -1, 1, -318645779, -25146803187525]\) | \(-2770540998624539614657/209924951154647363208\) | \(-271111350310116635073441084552\) | \([2]\) | \(314572800\) | \(4.3274\) | |
| 259182.fh4 | 259182fh2 | \([1, -1, 1, -98798459, 95018511723]\) | \(82582985847542515777/44772582831427584\) | \(57822356616188051279056896\) | \([2, 2]\) | \(78643200\) | \(3.6342\) | |
| 259182.fh5 | 259182fh1 | \([1, -1, 1, -76495739, 257212812651]\) | \(38331145780597164097/55468445663232\) | \(71635720864281089015808\) | \([2]\) | \(39321600\) | \(3.2877\) | \(\Gamma_0(N)\)-optimal |
| 259182.fh6 | 259182fh3 | \([1, -1, 1, 381058501, 747048148971]\) | \(4738217997934888496063/2928751705237796928\) | \(-3782389016468744260638599232\) | \([2]\) | \(157286400\) | \(3.9808\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.fh have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.fh do not have complex multiplication.Modular form 259182.2.a.fh
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.
