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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 193200bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.hp3 | 193200bu1 | \([0, 1, 0, -192008, -1843584012]\) | \(-12232183057921/22933241856000\) | \(-1467727478784000000000\) | \([2]\) | \(11943936\) | \(2.7405\) | \(\Gamma_0(N)\)-optimal |
| 193200.hp2 | 193200bu2 | \([0, 1, 0, -23744008, -44001664012]\) | \(23131609187144855041/322060536000000\) | \(20611874304000000000000\) | \([2]\) | \(23887872\) | \(3.0870\) | |
| 193200.hp4 | 193200bu3 | \([0, 1, 0, 1727992, 49762175988]\) | \(8915971454369279/16719623332762560\) | \(-1070055893296803840000000\) | \([2]\) | \(35831808\) | \(3.2898\) | |
| 193200.hp1 | 193200bu4 | \([0, 1, 0, -192944008, 1009495135988]\) | \(12411881707829361287041/303132494474220600\) | \(19400479646350118400000000\) | \([2]\) | \(71663616\) | \(3.6364\) |
Rank
sage: E.rank()
The elliptic curves in class 193200bu have rank \(0\).
Complex multiplication
The elliptic curves in class 193200bu do not have complex multiplication.Modular form 193200.2.a.bu
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
