Show commands:
SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 439569.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.ch1 | 439569ch2 | \([1, -1, 0, -143968005, 222576734628]\) | \(3885442650361/1996623837\) | \(169581089889669638251123533\) | \([2]\) | \(222953472\) | \(3.7251\) | |
439569.ch2 | 439569ch1 | \([1, -1, 0, -115396020, 476724541203]\) | \(2000852317801/2094417\) | \(177887046604188275418753\) | \([2]\) | \(111476736\) | \(3.3786\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.ch do not have complex multiplication.Modular form 439569.2.a.ch
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.