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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 28560.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.bq1 | 28560dc6 | \([0, -1, 0, -370720, 87001792]\) | \(1375634265228629281/24990412335\) | \(102360728924160\) | \([4]\) | \(262144\) | \(1.8144\) | |
| 28560.bq2 | 28560dc4 | \([0, -1, 0, -91600, -10640000]\) | \(20751759537944401/418359375\) | \(1713600000000\) | \([2]\) | \(131072\) | \(1.4678\) | |
| 28560.bq3 | 28560dc3 | \([0, -1, 0, -23920, 1272832]\) | \(369543396484081/45120132225\) | \(184812061593600\) | \([2, 4]\) | \(131072\) | \(1.4678\) | |
| 28560.bq4 | 28560dc2 | \([0, -1, 0, -5920, -152768]\) | \(5602762882081/716900625\) | \(2936424960000\) | \([2, 2]\) | \(65536\) | \(1.1213\) | |
| 28560.bq5 | 28560dc1 | \([0, -1, 0, 560, -12800]\) | \(4733169839/19518975\) | \(-79949721600\) | \([2]\) | \(32768\) | \(0.77468\) | \(\Gamma_0(N)\)-optimal |
| 28560.bq6 | 28560dc5 | \([0, -1, 0, 34880, 6494272]\) | \(1145725929069119/5127181719135\) | \(-21000936321576960\) | \([4]\) | \(262144\) | \(1.8144\) |
Rank
sage: E.rank()
The elliptic curves in class 28560.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 28560.bq do not have complex multiplication.Modular form 28560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
