Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 23184.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.bu1 | 23184bk2 | \([0, 0, 0, -3891, -426382]\) | \(-2181825073/25039686\) | \(-74768101761024\) | \([]\) | \(69120\) | \(1.3441\) | |
23184.bu2 | 23184bk1 | \([0, 0, 0, 429, 15122]\) | \(2924207/34776\) | \(-103840579584\) | \([]\) | \(23040\) | \(0.79475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.bu do not have complex multiplication.Modular form 23184.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.