Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2016n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2016.n2 | 2016n1 | \([0, 0, 0, 1887, -45740]\) | \(15926924096/28588707\) | \(-1333834713792\) | \([2]\) | \(3840\) | \(1.0114\) | \(\Gamma_0(N)\)-optimal |
2016.n1 | 2016n2 | \([0, 0, 0, -13548, -477920]\) | \(92100460096/20253807\) | \(60477543641088\) | \([2]\) | \(7680\) | \(1.3580\) |
Rank
sage: E.rank()
The elliptic curves in class 2016n have rank \(0\).
Complex multiplication
The elliptic curves in class 2016n do not have complex multiplication.Modular form 2016.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.