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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 195195.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 195195.bu1 | 195195bt6 | \([1, 0, 1, -515314804, -4502577363919]\) | \(3135316978843283198764801/571725\) | \(2759607375525\) | \([2]\) | \(17694720\) | \(3.1816\) | |
| 195195.bu2 | 195195bt4 | \([1, 0, 1, -32207179, -70354769119]\) | \(765458482133960722801/326869475625\) | \(1577736526772030625\) | \([2, 2]\) | \(8847360\) | \(2.8350\) | |
| 195195.bu3 | 195195bt5 | \([1, 0, 1, -32047474, -71086984603]\) | \(-754127868744065783521/15825714261328125\) | \(-76387700028006945703125\) | \([2]\) | \(17694720\) | \(3.1816\) | |
| 195195.bu4 | 195195bt3 | \([1, 0, 1, -4300209, 1809641017]\) | \(1821931919215868881/761147600816295\) | \(3673914089948500052655\) | \([2]\) | \(8847360\) | \(2.8350\) | |
| 195195.bu5 | 195195bt2 | \([1, 0, 1, -2022934, -1087963693]\) | \(189674274234120481/3859869269025\) | \(18630851726553291225\) | \([2, 2]\) | \(4423680\) | \(2.4885\) | |
| 195195.bu6 | 195195bt1 | \([1, 0, 1, 5911, -50818129]\) | \(4733169839/231139696095\) | \(-1115667165368610855\) | \([2]\) | \(2211840\) | \(2.1419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 195195.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 195195.bu do not have complex multiplication.Modular form 195195.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
