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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 139230dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139230.e4 | 139230dt1 | \([1, -1, 0, 101205, -74526075]\) | \(157253267277222479/3380108407603200\) | \(-2464099029142732800\) | \([2]\) | \(2457600\) | \(2.2093\) | \(\Gamma_0(N)\)-optimal |
| 139230.e3 | 139230dt2 | \([1, -1, 0, -2156715, -1154263419]\) | \(1521859549125225950641/90442622874240000\) | \(65932672075320960000\) | \([2, 2]\) | \(4915200\) | \(2.5559\) | |
| 139230.e2 | 139230dt3 | \([1, -1, 0, -6440715, 4857902181]\) | \(40532040527009362334641/9480591891166687200\) | \(6911351488660514968800\) | \([2]\) | \(9830400\) | \(2.9025\) | |
| 139230.e1 | 139230dt4 | \([1, -1, 0, -33999435, -76296714075]\) | \(5962265222680904006666161/23086248412500000\) | \(16829875092712500000\) | \([2]\) | \(9830400\) | \(2.9025\) |
Rank
sage: E.rank()
The elliptic curves in class 139230dt have rank \(0\).
Complex multiplication
The elliptic curves in class 139230dt do not have complex multiplication.Modular form 139230.2.a.dt
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.
