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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 91035.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.bs1 | 91035br6 | \([1, -1, 0, -60265224, 180085106533]\) | \(1375634265228629281/24990412335\) | \(439738487712320425335\) | \([2]\) | \(9437184\) | \(3.0872\) | |
| 91035.bs2 | 91035br4 | \([1, -1, 0, -14890779, -22112791790]\) | \(20751759537944401/418359375\) | \(7361571966746484375\) | \([2]\) | \(4718592\) | \(2.7406\) | |
| 91035.bs3 | 91035br3 | \([1, -1, 0, -3888549, 2622608968]\) | \(369543396484081/45120132225\) | \(793946832250274487225\) | \([2, 2]\) | \(4718592\) | \(2.7406\) | |
| 91035.bs4 | 91035br2 | \([1, -1, 0, -962424, -320487557]\) | \(5602762882081/716900625\) | \(12614789722216775625\) | \([2, 2]\) | \(2359296\) | \(2.3940\) | |
| 91035.bs5 | 91035br1 | \([1, -1, 0, 90981, -26166200]\) | \(4733169839/19518975\) | \(-343461501680523975\) | \([2]\) | \(1179648\) | \(2.0474\) | \(\Gamma_0(N)\)-optimal |
| 91035.bs6 | 91035br5 | \([1, -1, 0, 5670126, 13483175503]\) | \(1145725929069119/5127181719135\) | \(-90219365137925408772135\) | \([2]\) | \(9437184\) | \(3.0872\) |
Rank
sage: E.rank()
The elliptic curves in class 91035.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.bs do not have complex multiplication.Modular form 91035.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
