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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 215985bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215985.bp3 | 215985bu1 | \([1, 1, 0, -40537, 3124576]\) | \(4158523459441/16065\) | \(28460127465\) | \([2]\) | \(491520\) | \(1.2194\) | \(\Gamma_0(N)\)-optimal |
| 215985.bp2 | 215985bu2 | \([1, 1, 0, -41142, 3025719]\) | \(4347507044161/258084225\) | \(457211947725225\) | \([2, 2]\) | \(983040\) | \(1.5660\) | |
| 215985.bp4 | 215985bu3 | \([1, 1, 0, 30853, 12572256]\) | \(1833318007919/39525924375\) | \(-70022586111699375\) | \([2]\) | \(1966080\) | \(1.9126\) | |
| 215985.bp1 | 215985bu4 | \([1, 1, 0, -122817, -12835566]\) | \(115650783909361/27072079335\) | \(47959839938791935\) | \([2]\) | \(1966080\) | \(1.9126\) |
Rank
sage: E.rank()
The elliptic curves in class 215985bu have rank \(1\).
Complex multiplication
The elliptic curves in class 215985bu do not have complex multiplication.Modular form 215985.2.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 Cremona 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 Cremona labels.
