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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 339864.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 339864.bu1 | 339864bu3 | \([0, 1, 0, -7708304, 7483905456]\) | \(17418812548/1753941\) | \(5100311546134950319104\) | \([2]\) | \(17694720\) | \(2.9014\) | |
| 339864.bu2 | 339864bu2 | \([0, 1, 0, -1760684, -771391104]\) | \(830321872/127449\) | \(92652718398645291264\) | \([2, 2]\) | \(8847360\) | \(2.5549\) | |
| 339864.bu3 | 339864bu1 | \([0, 1, 0, -1689879, -846076218]\) | \(11745974272/357\) | \(16220714005365072\) | \([2]\) | \(4423680\) | \(2.2083\) | \(\Gamma_0(N)\)-optimal |
| 339864.bu4 | 339864bu4 | \([0, 1, 0, 3054056, -4245707488]\) | \(1083360092/3306177\) | \(-9614082073835899634688\) | \([2]\) | \(17694720\) | \(2.9014\) |
Rank
sage: E.rank()
The elliptic curves in class 339864.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 339864.bu do not have complex multiplication.Modular form 339864.2.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.
