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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 169280.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169280.bz1 | 169280ch3 | \([0, 0, 0, -226412, 41465136]\) | \(132304644/5\) | \(48508400107520\) | \([2]\) | \(788480\) | \(1.7121\) | |
| 169280.bz2 | 169280ch2 | \([0, 0, 0, -14812, 584016]\) | \(148176/25\) | \(60635500134400\) | \([2, 2]\) | \(394240\) | \(1.3655\) | |
| 169280.bz3 | 169280ch1 | \([0, 0, 0, -4232, -97336]\) | \(55296/5\) | \(757943751680\) | \([2]\) | \(197120\) | \(1.0190\) | \(\Gamma_0(N)\)-optimal |
| 169280.bz4 | 169280ch4 | \([0, 0, 0, 27508, 3309424]\) | \(237276/625\) | \(-6063550013440000\) | \([2]\) | \(788480\) | \(1.7121\) |
Rank
sage: E.rank()
The elliptic curves in class 169280.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 169280.bz do not have complex multiplication.Modular form 169280.2.a.bz
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.
