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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 5850.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.bq1 | 5850bj3 | \([1, -1, 1, -312005, 67157497]\) | \(294889639316481/260\) | \(2961562500\) | \([2]\) | \(24576\) | \(1.5498\) | |
| 5850.bq2 | 5850bj2 | \([1, -1, 1, -19505, 1052497]\) | \(72043225281/67600\) | \(770006250000\) | \([2, 2]\) | \(12288\) | \(1.2032\) | |
| 5850.bq3 | 5850bj4 | \([1, -1, 1, -15005, 1547497]\) | \(-32798729601/71402500\) | \(-813319101562500\) | \([2]\) | \(24576\) | \(1.5498\) | |
| 5850.bq4 | 5850bj1 | \([1, -1, 1, -1505, 8497]\) | \(33076161/16640\) | \(189540000000\) | \([2]\) | \(6144\) | \(0.85666\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 5850.bq do not have complex multiplication.Modular form 5850.2.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.
