Show commands:
SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 414400.fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414400.fb1 | 414400fb2 | \([0, -1, 0, -146433, -21035263]\) | \(169556172914/4353013\) | \(8914970624000000\) | \([2]\) | \(3538944\) | \(1.8428\) | \(\Gamma_0(N)\)-optimal* |
414400.fb2 | 414400fb1 | \([0, -1, 0, 1567, -1055263]\) | \(415292/469567\) | \(-480836608000000\) | \([2]\) | \(1769472\) | \(1.4962\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414400.fb have rank \(0\).
Complex multiplication
The elliptic curves in class 414400.fb do not have complex multiplication.Modular form 414400.2.a.fb
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.