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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 14490.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bq1 | 14490bt3 | \([1, -1, 1, -16592, -763891]\) | \(692895692874169/51420783750\) | \(37485751353750\) | \([2]\) | \(49152\) | \(1.3503\) | |
| 14490.bq2 | 14490bt2 | \([1, -1, 1, -3362, 61661]\) | \(5763259856089/1143116100\) | \(833331636900\) | \([2, 2]\) | \(24576\) | \(1.0037\) | |
| 14490.bq3 | 14490bt1 | \([1, -1, 1, -3182, 69869]\) | \(4886171981209/270480\) | \(197179920\) | \([4]\) | \(12288\) | \(0.65716\) | \(\Gamma_0(N)\)-optimal |
| 14490.bq4 | 14490bt4 | \([1, -1, 1, 6988, 359741]\) | \(51774168853511/107398242630\) | \(-78293318877270\) | \([2]\) | \(49152\) | \(1.3503\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.bq do not have complex multiplication.Modular form 14490.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
