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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 28314u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.d4 | 28314u1 | \([1, -1, 0, -21258, 24911860]\) | \(-822656953/207028224\) | \(-267370319974957056\) | \([2]\) | \(409600\) | \(2.0232\) | \(\Gamma_0(N)\)-optimal |
| 28314.d3 | 28314u2 | \([1, -1, 0, -1415178, 642418420]\) | \(242702053576633/2554695936\) | \(3299307971878473984\) | \([2, 2]\) | \(819200\) | \(2.3698\) | |
| 28314.d2 | 28314u3 | \([1, -1, 0, -2547738, -530234204]\) | \(1416134368422073/725251155408\) | \(936638636689673126352\) | \([2]\) | \(1638400\) | \(2.7163\) | |
| 28314.d1 | 28314u4 | \([1, -1, 0, -22585338, 41318763844]\) | \(986551739719628473/111045168\) | \(143411277584223792\) | \([2]\) | \(1638400\) | \(2.7163\) |
Rank
sage: E.rank()
The elliptic curves in class 28314u have rank \(1\).
Complex multiplication
The elliptic curves in class 28314u do not have complex multiplication.Modular form 28314.2.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 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.
