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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 203280.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.dk1 | 203280cm6 | \([0, -1, 0, -5903251240, -174574223474000]\) | \(3135316978843283198764801/571725\) | \(4148616039321600\) | \([2]\) | \(58982400\) | \(3.7912\) | |
| 203280.dk2 | 203280cm4 | \([0, -1, 0, -368953240, -2727629416400]\) | \(765458482133960722801/326869475625\) | \(2371867505081141760000\) | \([2, 2]\) | \(29491200\) | \(3.4447\) | |
| 203280.dk3 | 203280cm5 | \([0, -1, 0, -367123720, -2756020639568]\) | \(-754127868744065783521/15825714261328125\) | \(-114836349675572078400000000\) | \([2]\) | \(58982400\) | \(3.7912\) | |
| 203280.dk4 | 203280cm3 | \([0, -1, 0, -49261560, 70195294512]\) | \(1821931919215868881/761147600816295\) | \(5523125882264438319083520\) | \([2]\) | \(29491200\) | \(3.4447\) | |
| 203280.dk5 | 203280cm2 | \([0, -1, 0, -23173960, -42169216208]\) | \(189674274234120481/3859869269025\) | \(28008422859174699110400\) | \([2, 2]\) | \(14745600\) | \(3.0981\) | |
| 203280.dk6 | 203280cm1 | \([0, -1, 0, 67720, -1970406480]\) | \(4733169839/231139696095\) | \(-1677222179445777592320\) | \([2]\) | \(7372800\) | \(2.7515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.dk have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.dk do not have complex multiplication.Modular form 203280.2.a.dk
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
