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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 273273.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273273.o1 | 273273o3 | \([1, 0, 0, -91848884, 338804352249]\) | \(150902699857302457/59378319\) | \(33719121597981899079\) | \([2]\) | \(27869184\) | \(3.0951\) | |
273273.o2 | 273273o2 | \([1, 0, 0, -5767889, 5240496624]\) | \(37370253593737/730458729\) | \(414805052084049515889\) | \([2, 2]\) | \(13934592\) | \(2.7486\) | |
273273.o3 | 273273o1 | \([1, 0, 0, -757884, -131230737]\) | \(84778086457/35972937\) | \(20427924827908014417\) | \([2]\) | \(6967296\) | \(2.4020\) | \(\Gamma_0(N)\)-optimal |
273273.o4 | 273273o4 | \([1, 0, 0, 153026, 15487232123]\) | \(697864103/182466547263\) | \(-103617141716743585713783\) | \([2]\) | \(27869184\) | \(3.0951\) |
Rank
sage: E.rank()
The elliptic curves in class 273273.o have rank \(0\).
Complex multiplication
The elliptic curves in class 273273.o do not have complex multiplication.Modular form 273273.2.a.o
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.