Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 23184.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.be1 | 23184bw2 | \([0, 0, 0, -51915, 4482938]\) | \(5182207647625/91449288\) | \(273066110779392\) | \([2]\) | \(73728\) | \(1.5663\) | |
| 23184.be2 | 23184bw1 | \([0, 0, 0, -75, 200954]\) | \(-15625/5842368\) | \(-17445217370112\) | \([2]\) | \(36864\) | \(1.2197\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.be have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.be do not have complex multiplication.Modular form 23184.2.a.be
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.
