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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 244800.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.bu1 | 244800bu4 | \([0, 0, 0, -94190700, -351847406000]\) | \(30949975477232209/478125000\) | \(1427673600000000000000\) | \([2]\) | \(28311552\) | \(3.1943\) | |
| 244800.bu2 | 244800bu2 | \([0, 0, 0, -6062700, -5151854000]\) | \(8253429989329/936360000\) | \(2795955978240000000000\) | \([2, 2]\) | \(14155776\) | \(2.8477\) | |
| 244800.bu3 | 244800bu1 | \([0, 0, 0, -1454700, 589714000]\) | \(114013572049/15667200\) | \(46782008524800000000\) | \([2]\) | \(7077888\) | \(2.5011\) | \(\Gamma_0(N)\)-optimal |
| 244800.bu4 | 244800bu3 | \([0, 0, 0, 8337300, -25916654000]\) | \(21464092074671/109596256200\) | \(-327252667473100800000000\) | \([2]\) | \(28311552\) | \(3.1943\) |
Rank
sage: E.rank()
The elliptic curves in class 244800.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 244800.bu do not have complex multiplication.Modular form 244800.2.a.bu
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.
