Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 406560bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
406560.bi1 | 406560bi1 | \([0, -1, 0, -3186, -67164]\) | \(31554496/525\) | \(59524449600\) | \([2]\) | \(537600\) | \(0.86596\) | \(\Gamma_0(N)\)-optimal |
406560.bi2 | 406560bi2 | \([0, -1, 0, -161, -192399]\) | \(-64/2205\) | \(-16000172052480\) | \([2]\) | \(1075200\) | \(1.2125\) |
Rank
sage: E.rank()
The elliptic curves in class 406560bi have rank \(0\).
Complex multiplication
The elliptic curves in class 406560bi do not have complex multiplication.Modular form 406560.2.a.bi
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.