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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 271440.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271440.u1 | 271440u4 | \([0, 0, 0, -601429683, -5677084671118]\) | \(8057323694463985606146481/638717154543000\) | \(1907199203990925312000\) | \([2]\) | \(53084160\) | \(3.5292\) | |
| 271440.u2 | 271440u2 | \([0, 0, 0, -37669683, -88306287118]\) | \(1979758117698975186481/17510434929000000\) | \(52285878531035136000000\) | \([2, 2]\) | \(26542080\) | \(3.1827\) | |
| 271440.u3 | 271440u3 | \([0, 0, 0, -11386803, -209254844302]\) | \(-54681655838565466801/6303365630859375000\) | \(-18821748919896000000000000\) | \([2]\) | \(53084160\) | \(3.5292\) | |
| 271440.u4 | 271440u1 | \([0, 0, 0, -4077363, 908196338]\) | \(2510581756496128561/1333551278592000\) | \(3981962781055254528000\) | \([2]\) | \(13271040\) | \(2.8361\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271440.u have rank \(1\).
Complex multiplication
The elliptic curves in class 271440.u do not have complex multiplication.Modular form 271440.2.a.u
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.
