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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 16830cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.cl4 | 16830cy1 | \([1, -1, 1, -257, -5871]\) | \(-2565726409/19388160\) | \(-14133968640\) | \([2]\) | \(16384\) | \(0.63065\) | \(\Gamma_0(N)\)-optimal |
| 16830.cl3 | 16830cy2 | \([1, -1, 1, -6737, -210639]\) | \(46380496070089/125888400\) | \(91772643600\) | \([2, 2]\) | \(32768\) | \(0.97722\) | |
| 16830.cl1 | 16830cy3 | \([1, -1, 1, -107717, -13580391]\) | \(189602977175292169/1402500\) | \(1022422500\) | \([2]\) | \(65536\) | \(1.3238\) | |
| 16830.cl2 | 16830cy4 | \([1, -1, 1, -9437, -23799]\) | \(127483771761289/73369857660\) | \(53486626234140\) | \([4]\) | \(65536\) | \(1.3238\) |
Rank
sage: E.rank()
The elliptic curves in class 16830cy have rank \(0\).
Complex multiplication
The elliptic curves in class 16830cy do not have complex multiplication.Modular form 16830.2.a.cy
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.
