Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2016.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2016.k1 | 2016c3 | \([0, 0, 0, -2019, 34918]\) | \(2438569736/21\) | \(7838208\) | \([2]\) | \(1024\) | \(0.49067\) | |
| 2016.k2 | 2016c2 | \([0, 0, 0, -444, -3008]\) | \(3241792/567\) | \(1693052928\) | \([2]\) | \(1024\) | \(0.49067\) | |
| 2016.k3 | 2016c1 | \([0, 0, 0, -129, 520]\) | \(5088448/441\) | \(20575296\) | \([2, 2]\) | \(512\) | \(0.14410\) | \(\Gamma_0(N)\)-optimal |
| 2016.k4 | 2016c4 | \([0, 0, 0, 141, 2410]\) | \(830584/7203\) | \(-2688505344\) | \([2]\) | \(1024\) | \(0.49067\) |
Rank
sage: E.rank()
The elliptic curves in class 2016.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2016.k do not have complex multiplication.Modular form 2016.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
