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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 162288bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.dz4 | 162288bu1 | \([0, 0, 0, 32771445, -508544305094]\) | \(11079872671250375/324440155855872\) | \(-113975188129356089395249152\) | \([2]\) | \(44236800\) | \(3.6799\) | \(\Gamma_0(N)\)-optimal |
| 162288.dz2 | 162288bu2 | \([0, 0, 0, -790240395, -8146587987398]\) | \(155355156733986861625/8291568305839392\) | \(2912811624850990288234217472\) | \([2]\) | \(88473600\) | \(4.0265\) | |
| 162288.dz3 | 162288bu3 | \([0, 0, 0, -295861755, 13971941514538]\) | \(-8152944444844179625/235342826399858688\) | \(-82675471669216356834956279808\) | \([2]\) | \(132710400\) | \(4.2292\) | |
| 162288.dz1 | 162288bu4 | \([0, 0, 0, -10700357115, 423969404771626]\) | \(385693937170561837203625/2159357734550274048\) | \(758578121702296308055768301568\) | \([2]\) | \(265420800\) | \(4.5758\) |
Rank
sage: E.rank()
The elliptic curves in class 162288bu have rank \(1\).
Complex multiplication
The elliptic curves in class 162288bu do not have complex multiplication.Modular form 162288.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
